Over five days, a food truck sold 14, 19, 11, 23, and 18 burritos. What is the mean number of burritos sold per day?
Hint
The mean is the "fair share": add all the values, then divide by how many values there are.
Step-by-step solution
Add the five values:
14 + 19 + 11 + 23 + 18 = 85
Count the values: there are 5 days.
Divide the sum by the count:
\frac{85}{5} = 17
The mean is 17 burritos per day.
Check: If the truck sold exactly 17 every day, it would sell 17 \times 5 = 85 burritos — the same total ✓
Tip: The mean must lie between the smallest value (11) and the largest (23). Any answer outside that range — like 85 — is a sign you forgot to divide.
Question 2 of 36
Fill in
Luis worked these numbers of hours over 8 weeks:
35, 42, 28, 45, 40, 33, 38, 30
What is the median number of hours?
hours
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Put the numbers in order first. With an even number of values, there are two middle numbers.
Step-by-step solution
Put the values in order from least to greatest:
28,\ 30,\ 33,\ 35,\ 38,\ 40,\ 42,\ 45
There are 8 values (an even number), so there are two middle values — the 4th and 5th: 35 and 38.
The median is their mean:
\frac{35 + 38}{2} = \frac{73}{2} = 36.5
The median is 36.5 hours.
Check: Four values (28, 30, 33, 35) are below 36.5 and four (38, 40, 42, 45) are above ✓
Tip: Never take the middle of the list as written — always sort first. Here the unsorted middle values are 45 and 40, which would give the wrong answer, 42.5.
Question 3 of 36
The price of a gallon of regular gas at seven stations is:
$3.42, $3.59, $3.65, $3.59, $3.51, $3.38, $3.59
What is the range of the prices?
Hint
Range = greatest value − least value. Find those two values first; they are not necessarily first and last in the list.
Step-by-step solution
Find the greatest price: \$3.65.
Find the least price: \$3.38.
Subtract:
3.65 - 3.38 = 0.27
The range is $0.27.
Check: Every price lies between $3.38 and $3.65, and 3.38 + 0.27 = 3.65 ✓
Tip: Range measures spread — how far apart the data are. It uses only the two extreme values. Scan the whole list for the largest and smallest numbers; don't just use the first and last numbers.
Question 4 of 36
A swimmer timed four laps at practice. Her times were 1.8, 2.1, 1.9, and 2.2 minutes. What was her mean lap time?
Hint
Add the four times, then divide by the number of laps.
Step-by-step solution
Add the four lap times:
1.8 + 2.1 + 1.9 + 2.2 = 8.0
Count the values: there are 4 laps.
Divide the sum by the count (mean formula, on the GED formula sheet):
\text{mean} = \frac{8.0}{4} = 2.0
Her mean lap time was 2.0 minutes.
Check: The mean must be between the fastest time (1.8) and the slowest (2.2). It is: 1.8 < 2.0 < 2.2 ✓ Also, 2.0 \times 4 = 8.0, the same total.
Tip: Decimals do not change the method: add, then divide by how many values there are. Line up the decimal points when adding by hand, and count the values carefully before you divide.
Question 5 of 36
No calculatorFill in
At noon on one day, the temperatures in seven cities were:
58°F, 71°F, 64°F, 49°F, 77°F, 66°F, 60°F
What is the median temperature?
°F
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The median is the middle value, but only after the numbers are put in order.
Step-by-step solution
Put the temperatures in order from least to greatest:
49,\ 58,\ 60,\ 64,\ 66,\ 71,\ 77
Count the values: there are 7, an odd number, so there is exactly one middle value.
The middle position is \frac{7 + 1}{2} = 4th. The 4th value in the ordered list is 64.
The median temperature is 64°F.
Check: There are 3 values below 64 (49, 58, 60) and 3 values above it (66, 71, 77) ✓
Tip: Always sort first. The middle of the unsorted list here is 49, which is actually the coldest city. Cross off one value from each end at a time until one value is left; that is the median.
Question 6 of 36
No calculator
The overnight low temperatures in a Minnesota town for one week were:
-8°F, 5°F, -3°F, 12°F, 0°F, -11°F, 4°F
What is the range of these temperatures?
Hint
Range = greatest value minus least value. Which number is the least when some are negative?
Step-by-step solution
Find the greatest value: 12°F.
Find the least value. With negatives, the number farthest below zero is the least: -11°F (colder than -8°F).
Subtract least from greatest:
12 - (-11) = 12 + 11 = 23
The range is 23°F.
Check: On a number line, from -11 up to 0 is 11 degrees, and from 0 up to 12 is 12 more degrees: 11 + 12 = 23 ✓
Tip: Subtracting a negative is the same as adding its opposite. A range is a distance, so it can never be negative; if you get a negative number or a number smaller than the gap across zero, recheck your signs.
Question 7 of 36
Fill in
Keisha bowled four games with scores of 142, 165, 138, and 151. What score does she need in her fifth game so that her mean score for all five games is exactly 150?
Type your answer in the box. Fractions like 3/4 are fine.
Hint
A mean of 150 over 5 games means the five scores must add up to a certain total. What is that total?
Step-by-step solution
Total needed for a mean of 150 over 5 games:
5 \times 150 = 750
Total of the four games so far:
142 + 165 + 138 + 151 = 596
The fifth score must make up the difference:
750 - 596 = 154
Tip: For any "what score do I need" question: (target mean × total number of values) − (sum so far) = missing value. Don't just average the four scores and compare to 150.
Question 8 of 36
In Ms. Patel's class, the final grade is a weighted average:
Category
Weight
Ana's score
Tests
40%
85
Homework
35%
92
Final exam
25%
70
What is Ana's final grade?
Hint
Multiply each score by its weight (as a decimal), then add. The weights already add to 100%, so you do not divide by 3.
Step-by-step solution
Change each weight to a decimal: 40\% = 0.4, 35\% = 0.35, 25\% = 0.25.
Multiply each score by its weight:
0.4 \times 85 = 34 \qquad 0.35 \times 92 = 32.2 \qquad 0.25 \times 70 = 17.5
Add the products:
34 + 32.2 + 17.5 = 83.7
Ana's final grade is 83.7.
Check: The weights add to 0.4 + 0.35 + 0.25 = 1 ✓, and 83.7 lies between the lowest score (70) and the highest (92) ✓. It is a bit above the simple mean (82.3) because the low final-exam score counts the least.
Tip: In a weighted average, values with larger weights pull the result toward them. If the weights add to 100%, add the weighted products and stop; if they are counts (like 40 shirts), divide by the total count.
Question 9 of 36
The bar graph shows a town's monthly rainfall for six months.
What is the median monthly rainfall?
Hint
Write the six values from the bars, then put them in order. The months are in calendar order, not in order of size.
Step-by-step solution
Read the six bars: Jan 3.2, Feb 2.8, Mar 4.1, Apr 3.6, May 4.5, Jun 2.8 inches.
Put the values in order:
2.8,\ 2.8,\ 3.2,\ 3.6,\ 4.1,\ 4.5
With 6 values, the median is the mean of the 3rd and 4th values:
\frac{3.2 + 3.6}{2} = \frac{6.8}{2} = 3.4
The median rainfall is 3.4 inches.
Check: Three months (Feb, Jun, Jan) had less than 3.4 inches and three (Apr, Mar, May) had more ✓
Tip: A graph lists categories (here, months) in its own order. Before finding a median, re-list the values from least to greatest.
Question 10 of 36
Drop-down
The table shows the yearly salaries of the six employees of a small company.
Employee
1
2
3
4
5
6
Salary
$29,000
$31,000
$31,000
$34,000
$37,000
$126,000
Choose the correct answer for each blank.
The measure that best describes a typical salary at this company is the .
The mean salary is the median salary.
Choose an answer from each menu.
Hint
Find the mean and the median. Notice that one salary is very different from the rest.
Step-by-step solution
Mean: add the salaries (in thousands): 29 + 31 + 31 + 34 + 37 + 126 = 288. Divide by 6:
\frac{288}{6} = 48 \;\Rightarrow\; \$48{,}000
Median: the values are already in order. With 6 values, average the 3rd and 4th:
\frac{31 + 34}{2} = 32.5 \;\Rightarrow\; \$32{,}500
The $126,000 salary is an outlier. It pulls the mean up to $48,000 — more than five of the six people earn. The median ($32,500) is much closer to what most employees make, so it best describes a typical salary.
Since 48{,}000 > 32{,}500, the mean is greater than the median.
Check: Five of six employees earn less than the mean of $48,000 — so the mean is clearly not "typical" ✓
Tip: When data have an outlier or are skewed, the median is the better measure of center. A high outlier makes the mean greater than the median; a low outlier makes it smaller.
Question 11 of 36
The table shows the yearly salaries of the six employees of a small company.
Employee
1
2
3
4
5
6
Salary
$29,000
$31,000
$31,000
$34,000
$37,000
$126,000
The employee earning $126,000 leaves the company and is not replaced. By how much does the mean salary of the company decrease?
Hint
Find the mean before and the mean after. Remember that the number of employees changes too.
Step-by-step solution
Mean before (6 employees), in thousands:
\frac{29 + 31 + 31 + 34 + 37 + 126}{6} = \frac{288}{6} = 48
Mean after (5 employees):
\frac{29 + 31 + 31 + 34 + 37}{5} = \frac{162}{5} = 32.4
Check: The new total, 32.4 \times 5 = 162, plus the removed salary, 126, equals the old total 288 = 48 \times 6 ✓
Tip: Removing or adding a value changes both the sum and the count. Recompute the mean from scratch instead of trying to subtract a share of the removed value.
Question 12 of 36
Select all
A coffee shop counted the customers who came in during six different hours:
10, 6, 15, 9, 11, 9
Select all of the statements that are true.
Select all that apply.
Hint
Find all four measures carefully: sort the data first, and remember that range is a difference.
Step-by-step solution
Sort the data: 6, 9, 9, 10, 11, 15 (6 values).
Mean:\dfrac{6 + 9 + 9 + 10 + 11 + 15}{6} = \dfrac{60}{6} = 10. Statement A is true.
Median: the 3rd and 4th values are 9 and 10, so the median is \dfrac{9 + 10}{2} = 9.5. Statement B (median = 10) is false.
Mode: 9 appears twice, more than any other value. Statement C is true.
Range:15 - 6 = 9. Statement D is true, and statement E (range = 15) is false.
The true statements are A, C, and D.
Check: Mean 10 lies between 6 and 15 ✓; median 9.5 splits the data 3 and 3 ✓
Tip: In "select all" items with several measures, compute every measure once on your erasable note board, then check each statement against your list.
Question 13 of 36
In a county fair cooking contest, each dish is scored with these weights:
Category
Weight
Score for Rosa's chili
Taste
50%
88
Presentation
20%
75
Creativity
30%
90
What is Rosa's weighted score?
Hint
Change each percent to a decimal, multiply it by its own score, then add the results.
Step-by-step solution
Change each weight to a decimal: 50\% = 0.5, 20\% = 0.2, 30\% = 0.3. (They add to 1, so no extra division is needed.)
Multiply each score by its weight:
0.5 \times 88 = 440.2 \times 75 = 150.3 \times 90 = 27
Add the weighted parts:
44 + 15 + 27 = 86
Rosa's weighted score is 86.
Check: The answer must be between the lowest score (75) and the highest (90), and closer to 88 because taste counts the most. 86 fits ✓
Tip: A weighted average is not the plain mean of the scores (253 \div 3 \approx 84.3). The category with the biggest weight pulls the result toward its score.
Question 14 of 36
The bar graph shows the number of packages a delivery driver delivered each day last week.
What is the mean number of packages delivered per day?
Hint
Read the height of each of the five bars carefully (each gridline is 2 packages). Then find the mean.
Step-by-step solution
Read each bar (gridlines are every 2 packages; labels every 10):
Monday: 40
Tuesday: 36
Wednesday: 54
Thursday: 46
Friday: 48
Add the five values:
40 + 36 + 54 + 46 + 48 = 224
Divide by the number of days, 5:
\frac{224}{5} = 44.8
The mean is 44.8 packages per day.
Check:44.8 \times 5 = 224 ✓, and 44.8 is between the lowest bar (36) and the highest (54).
Tip: With a graph, the hardest part is reading the scale. Find what one gridline is worth before you read any bar. A mean does not have to be a whole number, even when every value is.
Question 15 of 36
Nine coworkers recorded their one-way commute times in minutes:
18, 22, 25, 20, 24, 19, 95, 21, 23
The mean is about 29.7 minutes and the median is 22 minutes. Which measure better describes a typical commute for this group, and why?
Hint
Look at where most of the values are. Is one value very different from the rest?
Step-by-step solution
Look at the data. Eight of the nine times are between 18 and 25 minutes. One time, 95 minutes, is far above the rest: an outlier.
Check the mean: \frac{18+22+25+20+24+19+95+21+23}{9} = \frac{267}{9} \approx 29.7 That is higher than 8 of the 9 values, because the 95 pulls it up.
Check the median: sorted, the times are 18, 19, 20, 21, \mathbf{22}, 23, 24, 25, 95. The middle (5th) value is 22, right in the cluster.
The median is not affected by how extreme the 95 is, so it better describes a typical commute.
The median (22 minutes), because the 95-minute outlier pulls the mean up.
Check: If the outlier were 35 instead of 95, the median would still be 22, but the mean would drop to 207 \div 9 = 23. The mean moves with the outlier; the median does not ✓
Tip: When a data set has an outlier or is lopsided (incomes, home prices, commute times), the median is usually the better "typical" value. When values are balanced with no outliers, the mean works well.
Question 16 of 36
Select all
A shoe store recorded the sizes of the first nine pairs of men's shoes it sold on Saturday:
8, 9.5, 10, 9.5, 11, 8.5, 9.5, 10, 12
Select all of the statements that are true.
Select all that apply.
Hint
Sort the sizes first. Then find the mode, median, range, and mean one at a time and test each statement.
"The mean and the median are both greater than 9" (9.78 and 9.5) ✓
"The median is 11" ✗ (11 is the middle of the unsorted list)
"The mean is less than the median" ✗ (9.78 > 9.5)
"Two sizes are tied for the mode" ✗ (9.5 appears 3 times; 10 only twice)
True: the mode is 9.5; the range is 4; the mean and median are both greater than 9.
Check:9.78 \times 9 \approx 88 ✓
Tip: For "select all" questions about a data set, compute every measure first, then judge the statements. Sorting once helps with the median, mode, and range at the same time.
Question 17 of 36
Fill in
A community center surveyed 30 families about how many children live in their home.
Number of children
0
1
2
3
4
Number of families
6
9
12
2
1
What is the mean number of children per family? Round to the nearest tenth.
children
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Each row of the table stands for many families. Multiply to find the total number of children, then divide by the total number of families.
Step-by-step solution
Multiply each number of children by how many families have it:
0 \times 6 = 0 \qquad 1 \times 9 = 9 \qquad 2 \times 12 = 24 \qquad 3 \times 2 = 6 \qquad 4 \times 1 = 4
Add to get the total number of children:
0 + 9 + 24 + 6 + 4 = 43
Add the frequencies to get the number of families:
6 + 9 + 12 + 2 + 1 = 30
Divide:
\frac{43}{30} \approx 1.433 \approx 1.4
The mean is about 1.4 children per family.
Check: The answer must be between 0 and 4, and most families have 1 or 2 children, so about 1.4 makes sense ✓
Tip: In a frequency table, do not average the top row (\frac{0+1+2+3+4}{5} = 2). Each value counts as many times as its frequency, so multiply first, then divide by the total frequency (30), not by the number of columns (5).
Question 18 of 36
In an evening algebra class, the final grade is computed as follows:
Category
Weight
Jamal's score
Quizzes
25%
84
Project
25%
90
Final exam
50%
?
What score does Jamal need on the final exam to earn a final grade of exactly 85?
Hint
Find how many points the quizzes and project already contribute. The exam must make up the rest, but remember it only counts 50%.
Step-by-step solution
Find what Jamal already has from the known categories:
0.25 \times 84 = 21 \qquad 0.25 \times 90 = 22.521 + 22.5 = 43.5
Let e be the exam score. The final grade is
43.5 + 0.5e = 85
Tip: For a "what score do I need" weighted question, write the weighted-average equation with a variable and solve. The last step is dividing by the weight; stopping before it (41.5) is a very common slip.
Question 19 of 36
A small bakery has 8 employees. Their hourly wages have a mean of $17.25, a median of $16.80, and a range of $6.40. The owner gives every employee a raise of $1.50 per hour.
Which statement about the new wages is true?
Hint
Imagine sliding every wage up by the same amount. Which measures slide up too, and which stay the same?
Step-by-step solution
Mean: if every value goes up by $1.50, the total goes up by 8 \times 1.50 = 12 and the count stays 8. The mean goes up by 12 \div 8 = \$1.50: new mean \$18.75.
Median: the order of the wages does not change, so the middle value(s) each go up by $1.50: new median \$18.30.
Range: the highest and lowest wages both go up by $1.50, so their difference stays the same: still \$6.40.
The mean and median each increase by $1.50, and the range stays $6.40.
Check: Try a tiny example: wages $10, $12, $16 (mean 12.67, median 12, range 6). Add $1.50: $11.50, $13.50, $17.50 (mean 14.17, median 13.50, range 6). Mean and median up $1.50, range unchanged ✓
Tip: Adding the same number to every value shifts the center (mean, median, mode) by that number but leaves the spread (range) unchanged. Multiplying every value by a number changes both.
Question 20 of 36
On a reading test, the 20 students in Class A had a mean score of 78. The 30 students in Class B had a mean score of 88. What is the mean score of all 50 students together?
Hint
The two classes are different sizes, so you cannot just average 78 and 88. Find each class's total points first.
Step-by-step solution
Find each class's total points (mean \times number of students):
\text{Class A: } 20 \times 78 = 1{,}560\text{Class B: } 30 \times 88 = 2{,}640
Add to get the total for all students:
1{,}560 + 2{,}640 = 4{,}200
Divide by the total number of students:
\frac{4{,}200}{50} = 84
The combined mean is 84.
Check: The answer is closer to 88 than to 78, which makes sense because Class B has more students ✓
Tip: To combine groups, never average the averages unless the groups are the same size. Go back to totals: total points \div total people.
Question 21 of 36
Fill in
Brianna's electric bills for the first five months of the year were $112, $98, $125, $104, and $131. She wants her mean monthly bill for the first six months to be no more than $115.
What is the most her sixth bill can be?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
A mean of $115 over 6 months means a certain total. How much of that total has she already used?
Step-by-step solution
A mean of $115 over 6 months allows a total of
6 \times 115 = \$690
Add the first five bills:
112 + 98 + 125 + 104 + 131 = \$570
The sixth bill can be at most the rest of the allowed total:
690 - 570 = \$120
Her sixth bill can be at most $120.
Check:(570 + 120) \div 6 = 690 \div 6 = 115 ✓ Any bill above $120 would push the mean above $115.
Tip: For any "missing value" mean problem, turn the target mean into a target total (mean \times count), then subtract what you already have. Remember to use the new count (6), not the old one (5).
Question 22 of 36
Fill in
The dot plot shows how many hours each member of a neighborhood cleanup club volunteered last month. Each dot is one member.
What is the median number of hours volunteered?
hours
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Count the dots to find how many members there are. Then count from the left to the middle dot.
Step-by-step solution
Count the dots above each number of hours:
Hours
1
2
3
4
5
6
7
Members
2
3
4
3
1
0
2
Total members: 2 + 3 + 4 + 3 + 1 + 0 + 2 = 15.
With 15 values, the median is the \frac{15 + 1}{2} = 8th value in order.
Count from the left: 1 hour covers values 1–2, 2 hours covers values 3–5, and 3 hours covers values 6–9. The 8th value is 3.
The median is 3 hours.
Check: 5 members volunteered less than 3 hours and 6 members volunteered more than 3 hours; with the 4 members at 3 hours, the middle member (8th) is at 3 ✓
Tip: A dot plot is already sorted from left to right, so you just count dots to the middle position. Don't pick the middle of the axis (4 hours) or the tallest stack unless it happens to contain the middle dot.
Question 23 of 36
No calculator
A youth soccer team scored these numbers of goals in its first 10 games:
2, 0, 3, 1, 2, 4, 1, 0, 2, 1
Which statement about the mode of the data is true?
Hint
Make a tally: how many times does each number of goals appear? Can more than one value be the mode?
Step-by-step solution
Tally how often each value appears:
Goals
0
1
2
3
4
Games
2
3
3
1
1
The mode is the value (or values) that appears most often. The highest count is 3.
Both 1 and 2 appear 3 times. When two values tie for most frequent, the data set has two modes (it is bimodal).
The data set has two modes: 1 goal and 2 goals.
Check: Recount from the original list: 1 appears in games 4, 7, 10 (3 times) and 2 appears in games 1, 5, 9 (3 times). No other value appears 3 times ✓
Tip: The mode is a data value, not the number of times it appears (3 here). A data set can have one mode, more than one mode, or no mode (if every value appears the same number of times).
Question 24 of 36
Fill in
A store sold T-shirts at three prices last month:
Price per shirt
Number sold
$11
42
$16
23
$24
15
What was the mean price of all the shirts sold? Round to the nearest cent.
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
This is a weighted average: each price counts as many times as the number of shirts sold at that price.
Step-by-step solution
Find the money taken in at each price:
11 \times 42 = 462 \qquad 16 \times 23 = 368 \qquad 24 \times 15 = 360
Total money:
462 + 368 + 360 = 1{,}190
Total number of shirts:
42 + 23 + 15 = 80
Mean price:
\frac{1{,}190}{80} = 14.875 \approx 14.88
The mean price was $14.88.
Check: The answer lies between $11 and $24 ✓, and is closer to $11 because most shirts (42) sold at $11. The simple mean of the three prices, \tfrac{11 + 16 + 24}{3} = 17, is too high because it ignores how many sold at each price.
Tip: Weighted average with counts = \dfrac{\sum(\text{value} \times \text{count})}{\sum \text{count}}. Divide by the number of items (80), not the number of prices (3).
Question 25 of 36
The mean of Tomás's first five test scores is 78. After he takes a sixth test, the mean of all six scores is 80. What did Tomás score on the sixth test?
Hint
Turn each mean into a total: mean × number of tests. The difference between the totals is the new score.
Step-by-step solution
Total of the first five tests:
5 \times 78 = 390
Total of all six tests:
6 \times 80 = 480
The sixth score is the difference:
480 - 390 = 90
Tomás scored 90 on the sixth test.
Check:\dfrac{390 + 90}{6} = \dfrac{480}{6} = 80 ✓
Tip: You don't need the individual scores: sum = mean \times count, always. Shortcut: the new score equals the new mean plus enough to lift each of the 5 earlier tests by 2 points: 80 + 5 \times 2 = 90.
Question 26 of 36
Drop-down
Seven students in a GED class took a practice test. Their scores were:
88, 91, 85, 90, 42, 87, 89
The mean score is about 81.7.
Choose the correct answer for each blank.
The outlier in this data set is . The outlier makes the mean the median, so the better describes a typical score.
Choose an answer from each menu.
Hint
Find the value far from the others. Then sort the data to find the median and compare it with the mean of 81.7.
Step-by-step solution
Outlier: six scores are between 85 and 91. The score 42 is far below them, so it is the outlier.
Median: sort the scores: 42, 85, 87, \mathbf{88}, 89, 90, 91. The middle (4th) value is 88.
Mean vs median: the mean is \frac{88 + 91 + 85 + 90 + 42 + 87 + 89}{7} = \frac{572}{7} \approx 81.7 That is less than the median of 88, because the low outlier drags the mean down.
Typical score: six of the seven students scored 85 or higher. The median (88) sits in that group; the mean (81.7) is lower than all six. The median better describes a typical score.
Outlier: 42. The mean is less than the median. The median is the better typical value.
Check: Without the 42, the mean would be 530 \div 6 \approx 88.3, very close to the median. The one low score moved the mean down by more than 6 points ✓
Tip: A low outlier pulls the mean down; a high outlier pulls it up. The median barely moves either way, so it is the safer "typical" value when an outlier is present.
Question 27 of 36
A community theater sold three kinds of tickets for its Saturday show:
Ticket type
Price
Tickets sold
Adult
$14
120
Child
$8
85
Senior
$10
45
What was the mean price paid per ticket?
Hint
Find the total money collected and the total number of tickets. Each price counts once for every ticket sold at that price.
Step-by-step solution
Find the money from each ticket type:
14 \times 120 = 1{,}680 \qquad 8 \times 85 = 680 \qquad 10 \times 45 = 450
Total money collected:
1{,}680 + 680 + 450 = \$2{,}810
Total tickets sold:
120 + 85 + 45 = 250
Mean price per ticket:
\frac{2{,}810}{250} = 11.24
The mean price was $11.24 per ticket.
Check: $11.24 is between the lowest price ($8) and the highest ($14), and closer to $14 because almost half of the tickets were adult tickets ✓
Tip: When a table shows how many of each value, the mean is a weighted average: total amount \div total count. Averaging the three prices (\frac{14 + 8 + 10}{3}) treats every ticket type as if it sold the same number.
Question 28 of 36
Fill in
A hospital scores job applicants for a nursing position using three parts:
Part
Weight
Score for Dana
Interview
40%
?
Written test
35%
76
References
25%
92
An applicant needs an overall score of at least 85 to be hired. What is the lowest interview score Dana can get and still be hired?
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Find the points Dana already has from the written test and references. Then set up an equation with the interview score as the unknown.
Step-by-step solution
Points from the known parts:
0.35 \times 76 = 26.6 \qquad 0.25 \times 92 = 2326.6 + 23 = 49.6
Let i be the interview score. For the lowest passing score, set the overall score equal to 85:
0.40i + 49.6 = 85
Subtract 49.6:
0.40i = 35.4
Divide by 0.40:
i = 88.5
The lowest interview score is 88.5.
Check:0.40(88.5) + 0.35(76) + 0.25(92) = 35.4 + 26.6 + 23 = 85 ✓ Any lower interview score would bring the total below 85.
Tip: "At least" questions are solved by finding the exact break-even value first. Make sure the weights add to 100% (40 + 35 + 25 = 100) and remember to divide by the unknown's weight at the end.
Question 29 of 36
Select all
A warehouse worker packed these numbers of boxes on five days:
12, 15, 15, 18, 20
On a sixth day she packs 16 boxes. Select all the measures that stay the same after the sixth day is included.
Select all that apply.
Hint
Find each measure before and after adding 16. Think about whether 16 is above, below, or equal to each measure.
Step-by-step solution
Before (5 days): 12, 15, 15, 18, 20
Mean: 80 \div 5 = 16
Median: 15 (3rd value)
Mode: 15
Range: 20 - 12 = 8
After (6 days): 12, 15, 15, 16, 18, 20
Mean: 96 \div 6 = 16 (same) ✓
Median: the middle two values are 15 and 16, so the median is \frac{15 + 16}{2} = 15.5 (changed) ✗
Mode: 15 still appears most often (same) ✓
Range: still 20 - 12 = 8 (same) ✓
The mean, the mode, and the range stay the same; only the median changes.
Check: The new value 16 equals the old mean, so it cannot pull the mean up or down. It lies between the old minimum and maximum, so the range cannot change ✓
Tip: Adding a value equal to the mean never changes the mean. Adding a value inside the current min-to-max interval never changes the range. The median is the most sensitive here because the count changed from odd (5) to even (6).
Question 30 of 36
A hiking club has 40 members with a mean age of 31 years. The 25 women in the club have a mean age of 34 years. What is the mean age of the men in the club?
Hint
Work with totals: find the total age of all members and the total age of the women. How many men are there?
Step-by-step solution
Total age of all 40 members:
40 \times 31 = 1{,}240
Tip: Group-mean problems are solved with totals, not by averaging means. Mean \times count = total; subtract totals to find the missing group, then divide by that group's own count.
Question 31 of 36
Over five days, the daily changes in Kevin's checking account balance were:
+$45.20, −$18.75, −$32.10, +$60.00, −$14.35
What was the mean daily change?
Hint
Keep the signs. Add the positive changes and the negative changes, combine them, then divide by the number of days.
The mean daily change was +$8.00 (an average gain of $8 per day).
Check: Over 5 days the balance went up $40 in total, and 5 \times \$8.00 = \$40.00 ✓
Tip: Negative values must keep their signs when you add. On the TI-30XS use the (-) key for each withdrawal: 45.2+(-)18.75+(-)32.1+60+(-)14.35, then divide the result by 5.
Question 32 of 36
A hospital recorded the weights, in pounds, of eight babies born on one day:
7.4, 6.9, 8.1, 7.0, 9.2, 6.5, 7.8, 7.3
What is the median weight?
Hint
Sort the weights first. With an even number of values, there are two middle values.
Step-by-step solution
Sort from least to greatest:
6.5,\ 6.9,\ 7.0,\ \mathbf{7.3},\ \mathbf{7.4},\ 7.8,\ 8.1,\ 9.2
There are 8 values (even), so the median is the mean of the 4th and 5th values: 7.3 and 7.4.
Average them:
\frac{7.3 + 7.4}{2} = \frac{14.7}{2} = 7.35
The median weight is 7.35 pounds.
Check: Four babies weigh less than 7.35 lb (6.5, 6.9, 7.0, 7.3) and four weigh more (7.4, 7.8, 8.1, 9.2) ✓
Tip: With an even count, the median is halfway between the two middle values, and it might not be one of the data values. Sorting first is essential: the two middle numbers of the unsorted list here are 7.0 and 9.2.
Question 33 of 36
Fill in
Six friends compared their scores on a typing test. Five of the scores, in words per minute, were 64, 81, 72, 90, and 77. The sixth friend had the lowest score of the group. The range of all six scores is 27.
What was the sixth friend's score?
words per minute
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Range = highest − lowest. Which score is the highest? Work backwards to find the lowest.
Step-by-step solution
The range formula is
\text{range} = \text{highest} - \text{lowest}
The sixth score is the lowest, so the highest score is among the five given: 90.
Substitute what you know:
27 = 90 - \text{lowest}
Solve:
\text{lowest} = 90 - 27 = 63
The sixth friend's score was 63 words per minute.
Check:63 is lower than all five other scores (the lowest of them is 64) ✓, and 90 - 63 = 27 ✓
Tip: In a work-backwards range problem, decide first which end (highest or lowest) is missing. Here, using the given minimum (64) by mistake would give 64 + 27 = 91, which would be the highest, contradicting the question.
Question 34 of 36
In a training course, the final grade is 60% test average and 40% homework average. Carlos has a homework average of 95. What is the lowest test average he can have and still earn a final grade of at least 80?
Hint
Write the weighted-average equation with the test average as the unknown, set it equal to 80, and solve.
Step-by-step solution
Let T be the test average. The final grade is:
0.6T + 0.4(95)
Set it equal to 80 (the lowest grade allowed):
0.6T + 38 = 80
Subtract 38 from both sides:
0.6T = 42
Divide by 0.6:
T = \frac{42}{0.6} = 70
The lowest test average is 70.
Check:0.6(70) + 0.4(95) = 42 + 38 = 80 ✓. Any test average below 70 would make the final grade less than 80.
Tip: "Work backwards" with a weighted average: write weight × value for every part, put the unknown in, and solve the equation. Because homework (95) is above the target, Carlos can afford a test average below 80.
Question 35 of 36
Drag and drop
At a community college, a grade of A is worth 4.0 points and a grade of B is worth 3.0 points. A student's GPA is the mean of the grade points, weighted by credits.
Course
Credits
Grade
Biology
4
A
English
3
B
Math
4
B
Art
1
A
Drag the correct value into each box. Not every value is used.
Total grade points
Total credits
GPA (to the nearest hundredth)
Tap a tile, then tap a box to place it.
Hint
Each course's grade points are credits × grade value. The GPA divides the total grade points by the total credits, not by the number of courses.
Step-by-step solution
Grade points for each course (credits \times grade value):
Biology: 4 \times 4.0 = 16
English: 3 \times 3.0 = 9
Math: 4 \times 3.0 = 12
Art: 1 \times 4.0 = 4
Total grade points:16 + 9 + 12 + 4 = 41
Total credits:4 + 3 + 4 + 1 = 12
GPA:\frac{41}{12} = 3.41\overline{6} \approx 3.42
Total grade points 41; total credits 12; GPA 3.42.
Check: The student has 5 credits of A and 7 credits of B, so the GPA must be between 3.0 and 4.0 and closer to 3.0. 3.42 fits ✓
Tip: A GPA is a weighted average: courses with more credits count more. Averaging the four letter grades as if they were equal (\frac{4 + 3 + 3 + 4}{4} = 3.50) gives too much weight to the 1-credit Art class.
Question 36 of 36
Fill in
A factory runs three shifts. The table shows the number of workers on each shift and the mean number of units each worker assembled on Monday.
Shift
Workers
Mean units per worker
Morning
18
46
Afternoon
12
41
Night
10
38
What was the mean number of units assembled per worker for all shifts combined?
units
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Find the total units for each shift (workers × mean). Then divide the grand total by the total number of workers.
Step-by-step solution
Total units for each shift:
\text{Morning: } 18 \times 46 = 828\text{Afternoon: } 12 \times 41 = 492\text{Night: } 10 \times 38 = 380
Grand total of units:
828 + 492 + 380 = 1{,}700
Total workers:
18 + 12 + 10 = 40
Combined mean:
\frac{1{,}700}{40} = 42.5
The combined mean is 42.5 units per worker.
Check: The plain average of the three shift means is (46 + 41 + 38) \div 3 \approx 41.7. Our answer is a bit higher, which makes sense because the biggest shift (morning) also has the highest mean ✓
Tip: With groups of different sizes, multiply each group mean by its group size to get totals, add them, and divide by the total size. This is the same idea as a weighted average, with the group sizes as the weights.
