If you are reviewing on the CSE Numerical Reasoning, you might have already encountered questions about mean, median, and mode. These are three kinds of “averages”. There are many averages in statistics but these are the three that are most common. Median, Mode and Mean questions appear on standardized tests in most High School, College, and some Nursing Entrance Tests. You will also likely encounter mean, median, and mode questions in the Numerical Reasoning portion of the Civil Service Exam.
The Mean
The “mean” is the “average” you’re used to, where you add up all the numbers and then divide by the number of numbers. Let’s use the numbers below as an example:
14, 19, 14, 15, 14, 17, 15, 22, 14
The “mean” is the usual average, so we’ll simply add all 9 numbers and then divide them by 9:
14 + 19 + 14 + 15 + 14 + 17 + 15 + 22 + 14 = 144 ÷ 9 = 16
The Median
The “median” is the “middle” value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median.
14, 14, 14, 14, 15, 15, 17, 19, 22
So the median in the set is 15.
The Mode
The “mode” is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list. In this case, 14 is repeated more than any number in the set so 14 is the mode. Note that it is possible not to have a most occurring number and then the answer becomes “No Mode”.
14 = occurred four times.
15 = occurred twice.
17, 19, 22 = occurred once
Piece of cake, right? Now let’s try finding the mean, mode, and median of another set of numbers:
2, 3, 5, 8
The mean is the usual average:
(2 + 3 + 5 + 8) ÷ 4 = 4.5
The median of any set is the middle number. In our example above, the numbers are already listed in numerical order so we don’t have to rewrite the list. But looking again at the set, you will notice that there is no “middle” number. When two numbers fall in the middle, you simply add the value of the two numbers and divide by 2 to get the middle of the two numbers. The middle two numbers in our example are 3 and 5, so:
(3 + 5) ÷ 2 = 4
Do you recognize the equation above? Yes, that’s PEMDAS.
Since the set presented (2, 3, 5, 8) are all unique and no data is repeated, there is no mode.
That’s it. I think you are now ready for some CSE mean, median, and mode exercises. Have your pen and paper ready and answer the practice questions that follow.
Mean, Median, and Mode Exercises
Here are some finding the mean, median, and mode exercise for you to put your newest knowledge to the test. If there are no multiple choices for a given question, then you have to manually solve the problem. Try to answer all 30 questions as fast and accurately as you can. That way when you encounter them on the Civil Service Exam, you won’t spend to much time answering them.
Find the mean, median, and mode of the given sets:
1. Find the mean of the data:
5, 34, 6, 17
2. Find the median of the set:
9, 7, 11, 13, 2, 18, 4, 5, 5
3. Find the mode of the data:
23, 18, 27, 29, 19, 21, 23, 28, 35, 16
4. Find the mean of the set:
0.8, 0.32, 0.45, 0.7, 0.23, 0.67, 0.12
5. Find the median of the data:
2.2, 10.2, 14.7, 5.9, 15.3, 4.9, 11.1, 10.5
6. Find the mean of the set:
1 1/4, 2 1/2, 5 1/2, 3 1/4, 2 1/2
7. Find the mean of the following data:
0, 5, 30, 25, 16, 18, 19, 26, 0, 20, 28
8. Find the median of the following data:
9, 6, 12, 5, 17, 3, 9, 5, 10, 2, 8, 7
9. Find the mode of the following data:
1, 20, 12, 5, 17, 3, 9, 5, 10, 2, 8, 6, 12, 19, 5, 0, 6, 5, 19, 18, 19, 26, 0, 7
10. Find the mean of the following data:
20, 24, 24, 24, 22, 22, 22, 23, 25
11. Find the mean of the even numbers:
2, 4, 6, 8, 10, 12, 14, 16, 28, 20
12. Find the median of the set of numbers:
21, 3, 7, 17, 19, 31, 46, 20, 43
13. Find the median of the set of numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
14. Find the median of the set of employee numbers:
9669, 6696, 9666, 6966, 9966, 6669, 9696, 6996
15. The following represents the age distribution of students in an elementary class. Find the mode of the values:
7, 9, 10, 13, 11, 7, 9, 19, 12, 11, 9, 7, 9, 10, 11
16. Find the mode from these test results:
88, 80, 77, 86, 88, 91, 77, 66, 69, 65, 43, 65, 75, 43, 88
17. Find the mode from these scores:
17, 19, 18, 15, 17, 18, 19, 11, 17, 15, 16, 19, 15, 17, 13, 11
18. Find the mean of these set of numbers:
100, 1050, 320, 600, 150
19. The following numbers represent the ages of people on a bus:
3, 6, 27, 13, 6, 8, 12, 20, 5, 10, 14. Find out the median.
20. These numbers are taken from the number of people that attended a particular church every Friday for 7 weeks:
62, 18, 39, 13, 16, 37, 25. Find the mean.
The table below shows the distribution of scores on exam No.8 in MTAP for Sections 01-08, March 2009. Refer to the table for exercises 21-24.
| Score |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
| Freq |
11 |
26 |
27 |
32 |
31 |
12 |
15 |
7 |
21. Select the statement that is correct.
- 6 people had scores of 11
- 27 people had scores of 10
- a and b are both correct
- All of these are false
22. Find the median quiz score
- 13.5
- 12
- 31.5
- 13
23. Find the mean quiz score. (Answers may have been rounded off).
- 12
- 12.2
- 13
- 13.4
24. Find the mode of the entire table.
- 31
- 7
- 12
- 14
The table below shows the distribution of ACT Math scores for a sample of students enrolled in MGF1106, Fall 1999. The data is authentic. Refer to the table for exercises 25-28.
25. Select the statement that is true.
- 17 students had scores of 10
- 42 students had scores of 13
- a and b are both true
- a, b, and c are all false
26. Find the mean ACT score (Answers may have been rounded off).
- 21
- 23
- 22
- 24
27. Find the median ACT score (Answers may have been rounded off).
- 21
- 23
- 22
- 24
28. Find the mode ACT score.
- 19
- 23
- 13
- The mode is not unique
The table below shows the relative frequency (R.F.) distribution of a population of video game store employees according to hourly wage.
| Wage |
$7.50 |
$8.00 |
$8.50 |
$9.00 |
$9.50 |
$10.00 |
| R. F. |
.49 |
.12 |
.17 |
.09 |
.07 |
.06 |
29. Find the mean wage (Answers may have been rounded off).
- $8.75
- $8.16
- $8.42
- $7.92
30. Find the median wage (Answers may have been rounded off).
- $7.50
- $8.00
- $8.50
- $7.75
Once you are done, you can click any of the social media buttons below to reveal the answer keys and assess your performance in solving mean, median, and mode exercises.
Mean, Median, and Mode Answer Keys
Here are the answers to this finding the mean, median, and mode practice test.
1. 15.5
5 + 34 + 6 + 17 = 15.5
2. 2, 4, 5, 5, 7, 9, 11, 13, 18 = 7
3. 16, 18, 19, 21, 23, 23, 27, 29, 28, 35 = 23
4. 0.8 + 0.32 + 0.45 + 0.7 + 0.23 + 0.67 + 0.12 = 0.47
5. 2.2, 4.9, 5.9, 10.2, 10.5, 11.1, 14.7, 15.3 >> 10.2 + 10.5 = 20.7 ÷ 2 = 10.35
6. You will also need to learn/know about adding fractions in order to solve this one correctly.
1 1/4 + 2 1/2 + 5 1/2 + 3 1/4 + 2 1/2 >> 15 ÷ 5 = 3
7. 0 + 5 + 30 + 25 + 16 + 18 + 19 + 26 + 0 + 20 + 28 = 187 ÷ 11 = 17
8. 2, 3, 5, 5, 6, 7, 8, 9, 9, 10, 12, 17 >> 7 + 8 = 15 ÷ 2 = 7.5
9. 5, 5, 5, 5, 6, 6, 0, 0, 12, 12, 19, 19, 19, 1, 2, 3, 7, 8, 9, 10, 17, 18, 20, 26 = 5 >> the data “5” occurred the most (4 times) than any other data in the set.
10. 20 + 24 + 24 + 22 + 22 + 24 + 22 + 23 + 25 = 206 ÷ 9 = 22.88
11. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 28 + 20 = 120 ÷ 10 = 12
12. 3, 7, 17, 19, 20, 21, 31, 43, 46 = 20
13. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 >> 5 + 6 = 11 ÷ 2 = 5.5
14. 6669, 6696, 6966, 6996, 9666, 9669, 9696, 9966 >> 6996 + 9666 = 16,662 ÷ 2 = 8331
15. 9, 9, 9, 9, 7, 7, 7, 11, 11, 11, 10, 10, 13, 19, 12 = 9 >> the data “9” occurred the most (4 times) than any other data in the set.
16. 88, 88, 88, 77, 77, 80, 65, 65, 43, 43, 86, 91, 66, 69, 75 = 88 >> the data “88” occurred the most (3 times) than any other data in the set.
17. 17, 17, 17, 17, 15, 15, 15, 19, 19, 19, 11, 11, 18, 18, 16, 13 = 17 >> the data “88” occurred the most (4 times) than any other data in the set.
18. 100 + 1,050 + 320 + 600 + 150 = 2220 ÷ 5 = 444
19. 3, 5, 6, 6, 8, 10, 12, 13, 14, 20, 27 = 10
20. 62 + 18 + 39 + 13 + 16 + 37 + 25 = 210 ÷ 7 = 30
21. B
22. B
23. B
24. C
25. D
26. A
27. A
28. D
29. B
30. B
So how many correct answers did you get right? I hope that this tutorial will make CSE mean, median, and mode questions easy for you to solve. For more Math related practice questions, head on over to these Civil Service Exam Numerical Reasoning reviewers.
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