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:

**2.**Find the median of the set:

**3.**Find the mode of the data:

**4.**Find the mean of the set:

**5.**Find the median of the data:

**6.**Find the mean of the set:

^{ 1}/

_{4}, 2

^{ 1}/

_{2}, 5

^{1}/

_{2}, 3

^{1}/

_{4}, 2

^{1}/

_{2}

**7.**Find the mean of the following data:

**8.**Find the median of the following data:

**9.**Find the mode of the following data:

**10.**Find the mean of the following data:

**11.**Find the mean of the even numbers:

**12.**Find the median of the set of numbers:

**13.**Find the median of the set of numbers:

**14.**Find the median of the set of employee numbers:

**15.**The following represents the age distribution of students in an elementary class. Find the mode of the values:

**16.**Find the mode from these test results:

**17.**Find the mode from these scores:

**18.**Find the mean of these set of numbers:

**19.**The following numbers represent the ages of people on a bus:

**20.**These numbers are taken from the number of people that attended a particular church every Friday for 7 weeks:

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

**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

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.