Mean, Median, Mode Questions

Introduction

Finding the median mean and mode is one of the first things you learn when studying statistics. The centre point of a data set can be described by these three metrics, which are referred to as measures of central tendency: mean, median, and mode.

Solving mean median mode problems in exams, real-world data analysis, and even business reporting requires an understanding of the mean median mode formula.This guide contains detailed definitions, formulas, and many mean median mode questions with solutions to help you practice and learn effectively.

 

Table of Contents

• What Are Mean, Median, and Mode?
• Mean Median Mode Formula
• Step-by-Step Examples
• Mean Median Mode Questions with Solutions
• Word Problems
• Practice Questions on Mean, Median, and Mode
• Tips for Solving Mean Median Mode Problems
• Conclusion
• FAQs on Mean Median Mode Questions

What Are Mean, Median, and Mode?

In statistics, the three most frequently used measures of central tendency are mean, median, and mode. They help in understanding the meaning of a set of numbers' typical or central value. Here’s what each one means:

Mean (Average)

Definition:
The mean is the sum of all values divided by the number of values.

Formula:
                  Sum of observations    

    Mean= ———————————— 

                  Number of observations

Example:
Data: 4, 6, 8, 10
Mean = (4 + 6 + 8 + 10) ÷ 4 = 28 ÷ 4 = 7

 

Median

Definition:
The median is the middle value when the numbers are arranged in ascending or descending order.

• If the number of values is odd → middle value

• If even → average of the two middle values
  
  

Example (Odd Number of Values):
Data: 3, 1, 5 → Ordered: 1, 3, 5 → Median = 3

Example (Even Number of Values):
Data: 2, 4, 6, 8 → Ordered: 2, 4, 6, 8 → Median = (4 + 6)/2 = 5

 

Mode

Definition:
The mode is the number that appears most frequently in the data set.

• One mode → Unimodal

• Two modes → Bimodal

• More than two → Multimodal

• No repetition → No mode
  
  

Example:
Data: 3, 4, 4, 5, 6, 4 → Mode = 4

Learning how to find the median mean and mode will help you interpret and summarize data effectively.

 

Mean Median Mode Formula

These mean median mode formula rules apply to most basic statistical questions.

 

Step-by-Step Examples

Example 1: Odd Number of Values

Data = [12, 15, 10, 18, 20]
Ordered = [10, 12, 15, 18, 20]

• Mean = (10+12+15+18+20)/5 = 15

• Median = 3rd value = 15

• Mode = No mode
  
  

Example 2: Even Number of Values

Data = [8, 10, 14, 18]

• Mean = (8+10+14+18)/4 = 12.5

• Median = (10 + 14)/2 = 12

• Mode = No mode

These help in understanding how to find the median mean and mode practically.

 

Example 3:

Data: 4, 8, 6, 5, 3

Step 1: Arrange the data in order
3, 4, 5, 6, 8

Mean = (3 + 4 + 5 + 6 + 8) ÷ 5 = 26 ÷ 5 = 5.2
Median = Middle value = 5
Mode = No repeated value → No mode

 

Example 4:

Data: 14, 16, 20, 18, 16, 22, 24

Step 1: Arrange in ascending order
14, 16, 16, 18, 20, 22, 24

Mean = (14 + 16 + 20 + 18 + 16 + 22 + 24) ÷ 7 = 130 ÷ 7 = 18.57
Median = 4th value = 18
Mode = 16 (appears twice)

 

Example 5:

Data: 30, 40, 50, 60, 70, 80, 90, 100

Step 1: Arrange in order (already done)
30, 40, 50, 60, 70, 80, 90, 100

Mean = (30 + 40 + 50 + 60 + 70 + 80 + 90 + 100) ÷ 8 = 520 ÷ 8 = 65
Median = (4th + 5th) ÷ 2 = (60 + 70) ÷ 2 = 65
Mode = No repeated value → No mode

 

Example 6:

Data: 11, 12, 13, 12, 14, 15, 12, 16

Step 1: Arrange in ascending order
11, 12, 12, 12, 13, 14, 15, 16

Mean = (11 + 12 + 13 + 12 + 14 + 15 + 12 + 16) ÷ 8 = 105 ÷ 8 = 13.13
Median = (4th + 5th) ÷ 2 = (12 + 13) ÷ 2 = 12.5
Mode = 12 (appears 3 times)

Example 7:

Data: 3, 5, 5, 5, 7, 9, 11, 13

Step 1: Arrange in ascending order (already done)
3, 5, 5, 5, 7, 9, 11, 13

Mean = (3 + 5 + 5 + 5 + 7 + 9 + 11 + 13) ÷ 8 = 68 ÷ 8 = 8.5
Median = (4th + 5th) ÷ 2 = (5 + 7) ÷ 2 = 6
Mode = 5 (appears 3 times)

 

Mean Median Mode Questions with Solutions

Let’s look at some commonly asked mean median mode questions with solutions.

Question 1:

Find the mean, median, and mode of the data set:
Data: 5, 8, 7, 5, 9, 10, 5

Step-by-step solution:

Mean:
Sum = 5 + 8 + 7 + 5 + 9 + 10 + 5 = 49
Number of values = 7
Mean = 49 ÷ 7 = 7

Median:
Arrange in order → 5, 5, 5, 7, 8, 9, 10
Middle value = 4th = 7

Mode:
Most frequent = 5 (appears 3 times)
Mode = 5

Final Answer:
Mean = 7, Median = 7, Mode = 5

 

Question 2:

Find the mean, median, and mode of:
Data: 12, 15, 20, 18, 15, 25, 30

Mean:
Sum = 12 + 15 + 20 + 18 + 15 + 25 + 30 = 135
Mean = 135 ÷ 7 = 19.29

Median:
Ordered data: 12, 15, 15, 18, 20, 25, 30
Middle value = 4th = 18

Mode:
Most frequent = 15 (appears twice)
Mode = 15

Final Answer:
Mean ≈ 19.29, Median = 18, Mode = 15

 

Question 3:

Find the mean using the direct method.

Formula:
Mean = ∑(fi × xi) / ∑fi

Step-by-step Table:

∑fi = 5 + 8 + 15 + 12 + 10 = 50
∑fi × xi = 1640

Mean = 1640 / 50 = 32.8

 

Question 4:

Find the mean using the assumed mean method. Take a = 40.

Step-by-step Table:

∑fi = 26
∑fidi = -40

Mean = 40 + (-40 / 26) = 40 - 1.54 = 38.46

 

Question 5:

n = 3 + 7 + 12 + 17 + 10 + 1 = 50, n/2 = 25
Cumulative frequency just above 25 = 39 → median class = 40 – 50

l = 40, F = 22, f = 17, h = 10

Median = 40 + [(25 – 22) / 17] × 10 = 40 + (3 / 17) × 10 = 40 + 1.76 = 41.76

 

Question 6:

Find the mode from the data:

Highest frequency = 15 → modal class = 30 – 40
l = 30, f1 = 15, f0 = 10, f2 = 8, h = 10

Mode = 30 + [(15 – 10) / (2×15 – 10 – 8)] × 10
Mode = 30 + [5 / (30 – 18)] × 10
Mode = 30 + (5 / 12) × 10 = 30 + 4.17 = 34.17

 

These are typical mean median mode questions with solutions from school and competitive exams.

 

Word Problems 

Problem 1:

A teacher recorded scores: 56, 67, 56, 78, and 90.
Find the mean, median, and mode.

• Mean = (56+67+56+78+90)/5 = 347/5 = 69.4

• Ordered = [56, 56, 67, 78, 90]

• Median = 67

• Mode = 56
  
  

Problem 2

The number of children in 7 families: [2, 3, 4, 3, 2, 5, 3]

• Mean = 22/7 = 3.14

• Ordered = [2, 2, 3, 3, 3, 4, 5]

• Median = 4th value = 3

• Mode = 3

These mean median mode problems demonstrate real-life usage.

 

Problem 3:

The table below shows the number of books read by 30 students in a month:

Find the mean number of books read using the direct method.

Solution:
Classmarks (xi): 2.5, 8, 13, 18, 23
fi: 4, 6, 10, 6, 4
fi × xi: 10, 48, 130, 108, 92
∑fi = 30, ∑fi × xi = 388
Mean = 388 ÷ 30 = 12.93

 

Problem 4:

The following table shows the ages of people in a village:

Find the median age.

Solution:
Total frequency = 40
n/2 = 20 → Median class = 30–40
l = 30, f = 12, F = 14, h = 10
Median = 30 + [(20 – 14) / 12] × 10 = 30 + 5 = 35

 

Problem 5:

A survey was conducted to know how many hours students study per day:

Find the mode of study hours.

Solution:
Modal class = 4–6
l = 4, f1 = 15, f0 = 9, f2 = 10, h = 2
Mode = 4 + [(15 – 9) / (2×15 – 9 – 10)] × 2
= 4 + (6 / 11) × 2 = 4 + 1.09 = 5.09 hours

 

Practice Questions on Mean, Median, and Mode

1. The weights of 6 children in kg are:
34, 38, 32, 40, 36, 35
Find the average (mean) weight.

 

2. A student scores 72, 78, 84, 66, and 90 marks in five subjects.
What is the average (mean) score?

 

3. A shoe store sold the following sizes most in a day:

7, 8, 9, 7, 10, 7, 9, 8, 7

Find the most popular shoe size (mode).

 

4. The following table shows the number of hours students studied in a week.
     Find the mean using the assumed mean method (a = 25).

 

5. The distribution below shows the scores of students in a test.
      Find the median score.

 

6. A survey of 50 houses shows the number of family members as follows.
    Find the mode of family size.

 

7. The ages of a group of 5 students are around a central value. Their ages are approximately equally spaced at 18, 20, 22, 24, and 26.

     Find the mean using step-deviation method. Take assumed mean = 22, class size = 2.

 

Tips for Solving Mean Median Mode Problems

• Always order the data set before calculating the median or identifying mode.

• Use the mean median mode formula carefully.

• For large data sets, double-check values and totals.

• Be aware of bimodal or multimodal data.

• Solve multiple mean median mode questions with solutions for practice.

Practicing various mean median mode problems sharpens your statistical thinking.

 

Conclusion 

In statistics, the mean, median, and mode are fundamental tools for interpreting data. The mode is the number that appears most frequently, the mean is the average, and the median is the middle value. Finding the median, mean, and mode makes it easier to solve problems in the real world and on tests. You can improve your skills and confidently solve data problems by practicing various mean median mode questions with answers and applying the proper mean median mode formula.

 

Related Links

Statistics - Explore the fundamentals of statistics, including data collection, analysis, and interpretation with easy-to-understand concepts.

Mean, Median, and Mode - Understand the measures of central tendency with definitions, formulas, and solved examples.

 

Frequently Asked Questions (FAQs) On Mean median mode questions

1. What is the mean mode and median?

• Mean is the average of all numbers.

• Median is the middle value when numbers are arranged in order.

• Mode is the number that appears most often.

 

2. What is the mean, median, and mode of 13, 16, 12, 14, 19, 12, 14, 13,14?

Ordered Data: 12, 12, 13, 13, 14, 14, 14, 16, 19

• Mean = (13 + 16 + 12 + 14 + 19 + 12 + 14 + 13 + 14) ÷ 9 = 127 ÷ 9 = 14.11

• Median = 5th number = 14

• Mode = 14 (appears 3 times)

 

3. What is the formula for mean median mode?

• Mean = (Sum of all values) ÷ (Number of values)

• Median = Middle value (or average of two middle values if even number of terms)

• Mode = Most frequent value in the data set
  
  

4. How to find a median?

1. Arrange the numbers in order.

2. If count is odd → pick the middle number.

3. If count is even → take the average of the two middle numbers.

 

5. What is the formula for mode?

• For simple data: Mode = value that occurs most frequently

• For grouped data:
  Mode = L + (f₁ − f₀) / (2f₁ − f₀ − f₂) × h
  Where:
  L = lower limit of modal class
  f₁ = frequency of modal class
  f₀ = frequency of class before
  f₂ = frequency of class after
  h = class width

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