Mean, Median and Mode Questions with Solutions | Class 9 and 10

Finding the mean, median 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, and mode problems, real-world data analysis, and even business reporting requires an understanding of the mean median mode formula. This page covers mean, median and mode questions for Class 9 and 10 students following the CBSE/NCERT curriculum containing detailed definitions, formulas, and many mean median and mode questions with solutions to help you practice and learn effectively.

Table of Contents

• What Are Mean, Median, and Mode?
• Mean Median Mode Formula
• Solved Examples with Step-by-Step Solutions
• Mean Median Mode Questions with Solutions
  • Easy Level (Questions 1-5)
  • Medium Level (Questions 6-10)
  • Hard Level - Grouped Data (Questions 11-15)
• Word Problems on Mean, Median and Mode
• Practice Questions on Mean, Median, and Mode
• Tips for Solving Mean Median Mode Problems
• Conclusion
• Frequently Asked Questions 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 describe the central value of a data set. Here's what each one means:

Mean (Average)

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

Formula: 

Mean = Sum of observations / Number of Observations

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

Read more about arithmetic mean

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

Read more about median

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

One Mode (Unimodal):
Data: 3, 4, 4, 5, 6, 4 - Mode = 4 (appears 3 times)

Two Modes (Bimodal):
Data: 2, 3, 3, 5, 7, 7, 9 - Mode = 3 and 7 (both appear twice)

More than Two Modes (Multimodal):
Data: 1, 1, 2, 3, 3, 4, 5, 5, 6 - Mode = 1, 3 and 5 (all appear twice)

No Mode:
Data: 10, 20, 30, 40, 50 - Mode = No mode (no value repeats)

Read more about mode

Mean Median Mode Formula

Formulas Table

Measure	Data Type	Formula	Variables / Description
Mean	Ungrouped Data	Mean = (Σx) / n	Σx = Sum of observations, n = Number of observations
Mean	Grouped Data (Direct Method)	Mean = (Σfᵢxᵢ) / Σfᵢ	fᵢ = Frequency, xᵢ = Midpoint (class mark)
Mean	Grouped Data (Assumed Mean Method)	Mean = a + (Σfᵢdᵢ / Σfᵢ)	a = Assumed mean, dᵢ = xᵢ - a
Mean	Grouped Data (Step-Deviation Method)	Mean = a + (Σfᵢuᵢ / Σfᵢ) × h	uᵢ = (xᵢ - a)/h, h = class width
Median	Ungrouped Data (Odd n)	Median = (n + 1)/2th observation	n = Number of observations
Median	Ungrouped Data (Even n)	Median = [(n/2)th observation + (n/2 + 1)th observation] / 2
Median	Grouped Data	Median = l + [(N/2 - cf)/f] × h	l = Lower boundary of median class, N = Total frequency, cf = Cumulative frequency before median class, f = Frequency of median class, h = Class width
Mode	Ungrouped Data	Mode = Most frequent value
Mode	Grouped Data	Mode = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h	l = Lower limit of modal class, f₁ = Frequency of modal class, f₀ = Frequency of class before, f₂ = Frequency of class after, h = Class width
Empirical Relation	-	Mode = 3 × Median - 2 × Mean	Used for moderately skewed distributions
Alternative Empirical Relation	-	Mean - Mode = 3 (Mean - Median)	Rearranged version of above

Learn more about mean, median and mode

Solved Examples with Step-by-Step Solutions

Example 1: Odd Number of Values

Data: 12, 15, 10, 18, 20

Step 1: Arrange the data in ascending order
Ordered = [10, 12, 15, 18, 20]

Step 2: Find the Mean
Mean = (10 + 12 + 15 + 18 + 20) ÷ 5 = 75 ÷ 5 = 15

Step 3: Find the Median
Number of values = 5 (odd) - Middle value = 3rd value
Median = 15

Step 4: Find the Mode
No value repeats - Mode = No mode

Example 2: Even Number of Values

Data: 8, 10, 14, 18

Step 1: Arrange the data in ascending order
Ordered = [8, 10, 14, 18]

Step 2: Find the Mean
Mean = (8 + 10 + 14 + 18) ÷ 4 = 50 ÷ 4 = 12.5

Step 3: Find the Median
Number of values = 4 (even) - Average of 2nd and 3rd values
Median = (10 + 14) ÷ 2 = 12

Step 4: Find the Mode
No value repeats - Mode = No mode

Example 3:

Data: 4, 8, 6, 5, 3

Step 1: Arrange the data in ascending order
Ordered = [3, 4, 5, 6, 8]

Step 2: Find the Mean
Mean = (3 + 4 + 5 + 6 + 8) ÷ 5 = 26 ÷ 5 = 5.2

Step 3: Find the Median
Number of values = 5 (odd) - Middle value = 3rd value
Median = 5

Step 4: Find the Mode
No value repeats - Mode = No mode

Example 4:

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

Step 1: Arrange the data in ascending order
Ordered = [14, 16, 16, 18, 20, 22, 24]

Step 2: Find the Mean
Mean = (14 + 16 + 20 + 18 + 16 + 22 + 24) ÷ 7 = 130 ÷ 7 = 18.57

Step 3: Find the Median
Number of values = 7 (odd) - Middle value = 4th value
Median = 18

Step 4: Find the Mode
16 appears twice - Mode = 16

Example 5:

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

Step 1: Arrange the data in ascending order
Ordered = [30, 40, 50, 60, 70, 80, 90, 100]

Step 2: Find the Mean
Mean = (30 + 40 + 50 + 60 + 70 + 80 + 90 + 100) ÷ 8 = 520 ÷ 8 = 65

Step 3: Find the Median
Number of values = 8 (even) - Average of 4th and 5th values
Median = (60 + 70) ÷ 2 = 65

Step 4: Find the Mode
No value repeats - Mode = No mode

Example 6:

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

Step 1: Arrange the data in ascending order
Ordered = [11, 12, 12, 12, 13, 14, 15, 16]

Step 2: Find the Mean
Mean = (11 + 12 + 13 + 12 + 14 + 15 + 12 + 16) ÷ 8 = 105 ÷ 8 = 13.13

Step 3: Find the Median
Number of values = 8 (even) - Average of 4th and 5th values
Median = (12 + 13) ÷ 2 = 12.5

Step 4: Find the Mode
12 appears 3 times - Mode = 12

Example 7:

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

Step 1: Arrange the data in ascending order
Ordered = [3, 5, 5, 5, 7, 9, 11, 13]

Step 2: Find the Mean
Mean = (3 + 5 + 5 + 5 + 7 + 9 + 11 + 13) ÷ 8 = 58 ÷ 8 = 7.25

Step 3: Find the Median
Number of values = 8 (even) - Average of 4th and 5th values
Median = (5 + 7) ÷ 2 = 6

Step 4: Find the Mode
5 appears 3 times - Mode = 5

Read more:

• Profit and Loss Questions
• Percentage Questions
• HCF and LCM Questions
• BODMAS Rule Questions
• LCM Questions
  
  

Mean Median Mode Questions with Solutions

Easy Level

Question 1: Find the mean of: 15, 20, 25, 30, 35

Solution:
Sum = 15 + 20 + 25 + 30 + 35 = 125
Number of values = 5
Mean = 125 ÷ 5 = 25

Question 2: Find the mode of: 4, 5, 4, 3, 2, 4, 5, 3, 4

Solution:
4 appears 4 times - most frequent value.
Mode = 4

Question 3: Find the median of: 11, 7, 3, 15, 9

Solution:
Arranged in order: 3, 7, 9, 11, 15
Number of values = 5 (odd)
Middle value = 3rd value
Median = 9

Question 4: If the mean of 5 numbers is 18, what is their sum?

Solution:
Mean = Sum ÷ Number of values
18 = Sum ÷ 5
Sum = 18 × 5 = 90

Question 5: Find the mean, median, and mode of: 6, 8, 6, 10, 12, 8, 6

Solution:
Arranged: 6, 6, 6, 8, 8, 10, 12
Mean = (6+8+6+10+12+8+6) ÷ 7 = 56 ÷ 7 = 8
Median = 4th value = 8
Mode = 6 (appears 3 times)
Answer: Mean = 8, Median = 8, Mode = 6

Medium Level

Question 6: The mean of 6 observations is 12. Five of them are 10, 14, 8, 16, 11. Find the sixth observation.

Solution:
Total sum = 12 × 6 = 72
Sum of 5 known values = 10 + 14 + 8 + 16 + 11 = 59
Sixth observation = 72 - 59 = 13

Question 7: Find the median of: 23, 45, 12, 67, 34, 89, 56, 21

Solution:
Arranged: 12, 21, 23, 34, 45, 56, 67, 89
Number of values = 8 (even)
Median = (4th + 5th) ÷ 2 = (34 + 45) ÷ 2 = 79 ÷ 2 = 39.5

Question 8: The mode of a data set is 7. The data is: 5, 7, 3, 7, x, 7, 9. Find x.

Solution:
7 already appears 3 times and is the mode regardless of x.
x should not create another mode - x can be any value other than 5, 3, or 9.
x = 2 (or any value that does not appear more than 3 times)

Question 9: Find the mean, median, and mode of the first 10 natural numbers.

Solution:
Data: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Mean = 55 ÷ 10 = 5.5
Median = (5th + 6th) ÷ 2 = (5+6) ÷ 2 = 5.5
Mode = No mode (all values appear once)
Answer: Mean = 5.5, Median = 5.5, Mode = No mode

Question 10: If mode = 65 and mean = 61.5, find the median using the empirical formula.

Solution:
Mode = 3 × Median - 2 × Mean
65 = 3 × Median - 2 × 61.5
65 = 3 × Median - 123
3 × Median = 188
Median = 188 ÷ 3 = 62.67

Hard Level (Grouped Data)

Question 11: Find the mean, median, and mode of the data set:

Class	Frequency
0-10	3
10-20	7
20-30	12
30-40	10
40-50	8

Mean (Direct Method):

Class	fi	xi	fi × xi
0-10	3	5	15
10-20	7	15	105
20-30	12	25	300
30-40	10	35	350
40-50	8	45	360

∑fi = 40, ∑fi × xi = 1130

Mean = 1130 ÷ 40 = 28.25

Median:
n = 40, n/2 = 20 - Median class = 20-30
l = 20, f = 12, cf = 10, h = 10
Median = 20 + [(20-10)/12] × 10 = 20 + 8.33 = 28.33

Mode:
Highest frequency = 12 - Modal class = 20-30
l = 20, f1 = 12, f0 = 7, f2 = 10, h = 10
Mode = 20 + [(12-7)/(24-7-10)] × 10 = 20 + (5/7) × 10 = 27.14

Empirical Verification:
3 × Median - 2 × Mean = 3 × 28.33 - 2 × 28.25 = 84.99 - 56.5 = 28.49 ≈ Mode [which is correct]

Question 12: Find the mean using the step deviation method. Take a = 30, h = 10.

Class	fi	xi	ui = (xi-30)/10	fi × ui
10-20	4	15	-2	-8
20-30	8	25	-1	-8
30-40	14	35	0	0
40-50	10	45	1	10
50-60	4	55	2	8

∑fi = 40, ∑fi × ui = 2
Mean = 30 + (2/40) × 10 = 30 + 0.5 = 30.5

Question 13: Find the median from this distribution:

Class Interval	Frequency
0 - 10	5
10 - 20	8
20 - 30	20
30 - 40	10
40 - 50	7

n = 50, n/2 = 25 - Median class = 20-30
l = 20, f = 20, cf = 13, h = 10
Median = 20 + [(25-13)/20] × 10 = 20 + 6 = 26

Question 14: Find the mode from this distribution:

Class Interval	Frequency
5 - 15	6
15 - 25	11
25 - 35	21
35 - 45	9
45 - 55	3

Highest frequency = 21 - Modal class = 25-35
l = 25, f1 = 21, f0 = 11, f2 = 9, h = 10
Mode = 25 + [(21-11)/(42-11-9)] × 10 = 25 + (10/22) × 10 = 25 + 4.55 = 29.55

Question 15: The mean of a grouped data is 53. The median is 50.4. Find the mode using the empirical relation.

Mode = 3 × Median - 2 × Mean
Mode = 3 × 50.4 - 2 × 53
Mode = 151.2 - 106 = 45.2

Word Problems on Mean, Median and Mode

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

Problem 3: The table below shows the number of books read by 30 students in a month:

Books Read	Number of Students
0 - 5	4
6 - 10	6
11 - 15	10
16 - 20	6
21 - 25	4

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:

Age Group	Frequency
0-10	2
10-20	4
20-30	8
30-40	12
40-50	9
50-60	5

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:

Hours Studied	Number of Students
0 - 2	5
2 - 4	9
4 - 6	15
6 - 8	10
8 - 10	6

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. Find the mean of: 5, 10, 15, 20, 25, 30

2. Find the mode of: 3, 5, 7, 5, 9, 5, 3, 7, 5

3. Find the median of: 42, 38, 55, 29, 61

4. The mean of 8 numbers is 35. Seven of them are 28, 31, 40, 36, 29, 38, 42. Find the eighth number.

5. Find the median of: 102, 98, 87, 115, 76, 134, 91, 110

6. If mean = 40 and median = 42, find the mode using the empirical formula.

7. The ages of 7 students are: 14, 16, 15, 14, 17, 14, 16. Find the mean, median, and mode.

8. Find the mean using the assumed mean method (a = 25):

Class	Frequency
0 - 10	2
10 - 20	6
20 - 30	10
30 - 40	8
40 - 50	4

9. Find the median:

Class	Frequency
10 - 20	4
20 - 30	9
30 - 40	15
40 - 50	12
50 - 60	6

10. Find the mode:

Class	Frequency
20 - 30	5
30 - 40	12
40 - 50	18
50 - 60	10
60 - 70	4

Answers to practice questions

1. 17.5
2. 5
3. 42
4. 36
5. 100.5
6. 46
7. Mean = 15.14, Median = 15, Mode = 14
8. Mean = 26
9. Median = 35.33
10. Mode = 45.83
    
    

Tips for Solving Mean, Median and 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.
  
  

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.

Frequently Asked Questions on Mean Median and Mode questions

1. What is the difference between mean, median and mode?

Answer: Mean is the average of all values, calculated by dividing the sum by the count. Median is the middle value when data is arranged in order. Mode is the value that appears most frequently. Each measures central tendency differently - mean uses all values, median uses position, mode uses frequency.

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

Answer: 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 and mode?

Answer: 

• 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?

Answer: 

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?

Answer: 

• 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

6. When should you use mean, median or mode?"

Answer: Use mean when data has no extreme values and all values matter equally. Use median when data has outliers or is skewed - for example, income data. Use mode when you need the most common value - for example, the most popular shoe size or exam score.

Master maths concepts like mean, median, and mode with Orchids The International School.