# Learn Mean, Median and Mode – Tutorial and Practice Questions

- Posted by Brian Stocker MA
- Date April 7, 2014
- Comments 11 comments

## Mean, Median and Mode

Median, Mode and Mean questions appear on standardized tests in most High School, and some Nursing Entrance Tests

### Audio Version of this Post

### Mean, Median and Mode – Quick Review and Tutorial

## Mean, Median and Mode

Mean, mode and median are basic statistical tools used to calculate different types of averages. Below is a quick tutorial followed by practice questions.

**Mean**

Mean is the most common form of average used. To calculate mean, you simple add up all the values of data given and divide by the number data provided.

**Example**

Find the mean of 8, 5, 7, 10, 15, 21

Sum of values = 8 + 5 + 7 + 10 + 15 + 21 = 66

Number of data = 6

Mean = 66/6 = 11

**Median**

Median refers to the middle value among a set or series of values after they have been arranged in numerical order. Median thus means the middle of the set of values. When two numbers fall in the middle, you simple add the value of the two numbers and divide by 2 to get the middle of the two numbers.

**Example**

Arrange these numbers in ascending order and then find the median

First arrange in ascending order 8, 5, 7, 10, 15, 21

= 5, 7, 8, 10, 15, 21

There are 6 numbers on the series and two fall in the middle = 8 and 10

The median = 8 + 10/2 = 18/2 =9

**Mode**

Mode refers to the most occurring number or value among a set of values. Note that it is possible not to have a most occurring number and then the answer becomes ‘No Mode’

**Example**

8, 5, 7, 10, 15, 21, 5, 7, 2, 5

Mode refers to the most occurring number 8, 10, 15, 2 and 21 occur once

5 occurs 3 times

7 occurs 2 times

The most occurring number is 5, which occurs three times.

### Statistics Practice Questions

### Practice Questions

**1. Find the median of the set of numbers: 1,2,3,4,5,6,7,8,9 and 10.**

a. 55

b. 10

c. 1

d. 5.5

**2. Find the median of the set of numbers: 21, 3, 7, 17, 19, 31, 46, 20 and 43.**

a. 19

b. 20

c. 3

d. 167

**3. Find the median of the set of numbers: 100, 200, 450, 29, 1029, 300 and 2001.**

a. 300

b. 29

c. 7

d. 4,080

**4. The following represents 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.**

a. 7

b. 9

c. 10

d. 11

**5. Find the mode from these test results: 90, 80, 77, 86, 90, 91, 77, 66, 69, 65, 43, 65, 75, 43, 90.**

a. 43

b. 77

c. 65

d. 90

**6. Find the mode from these test results: 17, 19, 18, 17, 18, 19, 11, 17, 16, 19, 15, 15, 15, 17, 13, 11.**

a. 15

b. 11

c. 17

d. 19

**7. Find the mean of these set of numbers: 100, 1050, 320, 600 and 150.**

a. 333

b. 444

c. 440

d. 320

**8. The following numbers represent the ages of people on a bus: 3, 6, 27, 13, 6, 8, 12, 20, 5, 10. Calculate their mean of their ages.**

a. 11

b. 6

c. 9

d. 110

**9. 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.**

a. 25

b. 210

c. 62

d. 30

### Answer Key

**1. D**

First arrange the numbers in a numerical sequence: 1,2,3,4,5,6,7,8,9, 10. Then find the middle number or numbers. The middle numbers are 5 and 6. The median = 5 + 6/2 = 11/2 = 5.5

**2. B**

First arrange the numbers in a numerical sequence: 3,7, 17, 19, 20, 21, 31, 43, 46. Next find the middle number. The median = 20

**3. A**

First arrange the numbers in a numerical sequence: 29,100, 200, 300, 450, 1029, 2001. Next find the middle number. The median = 300

**4. B**

Simply find the most recurring number. The most occurring number in the series is 9

**5. D**

Simply find the most recurring number. The most occurring number in the series is 90.

**6. C**

Simply find the most recurring number. The most occurring number in the series is 17.

**7. B**

First add all the numbers 100 + 1050 + 320 + 600 + 150 = 2220. Then divide by 5 (the number of data provided) = 2220/5 = 444

**8. A**

First add all the numbers 3 + 6 + 27 + 13 + 6 + 8 + 12 + 20 + 5 + 10 = 110. Then divide by 10 (the number of data provided) = 110/10 = 11

**9. D**

First add all the numbers 62 + 18 + 39 + 13 + 16 + 37 + 25 = 210. Then divide by 7 (the number of data provided) = 210/7 = 30

### Common Mistakes Calculating Mean, Median, and Mode

**Calculating Mean:**Not adding up all the numbers correctly and dividing by the wrong number of elements.**Calculating Median:**Ordering incorrectly; not understanding the difference between the median and the average.

The median is the mid-point number, where half the elements fall above and half below.

The mean (or “average”) is the sum of all data divided by the number of data points.**Calculating the Mode:**Incorrectly identifying the most frequently occurring number(s) or not understanding that a set of data may have multiple modes or no mode at all.**Not understanding outliers:**Extreme values have a huge effect on the mean, but have less impact on the median and mode.**Not understanding the difference between sample and population:**The formulas and methods used to calculate measures of central tendency can be different for sample and population.

### Mean Mode and Median Video Tutorial

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Monday, April 7th, 2014

**Date Modified:**Friday, June 14th, 2024

Tag:Average, Mean, Median, Mode, Practice Questions

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## 11 Comments

That dash before the number throws you off, I assumed they were negative numbers.

Good point and thanks! I have changed to semi colon.

With the “and” it made it a little harder to order.

It is good and helps to prepare for exams

it was super easy

its a good website – thanks!

this is a great practice i have a test today on it and you just saved my life

It was so easy

We need difficult ones

Thanks, I got to practice these sums

hi, what is the answer for this

Find the mean of the following distribution. X 1 2 3 4 5 F 4 5 8 10 3

please tell till 3:00 pm

u r good thanks