Statistics — Class 9 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Statistics" — 7 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Statistics" — 7 important questions with detailed answers for CBSE board exam prepa…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

Define mean, median, and mode for a set of data. For the data set {12, 15, 12…
For the frequency distribution: Class 0-10 (frequency 5), 10-20 (frequency 8)…
Construct a frequency distribution table and draw a bar graph for the followi…
For the data {2, 4, 6, 8, 10}, calculate the mean, median, and verify that fo…
The data shows test scores of 10 students: 70, 75, 80, 85, 80, 90, 85, 95, 80…
Create a grouped frequency distribution for the following age data (in years)…
+ 1 more questions in the full chapter

Solutions Summary:

Question	Status
Define mean, median, and mode for a set of data. For the …	✓ Solved
For the frequency distribution: Class 0-10 (frequency 5),…	✓ Solved
Construct a frequency distribution table and draw a bar g…	✓ Solved
For the data {2, 4, 6, 8, 10}, calculate the mean, median…	✓ Solved
The data shows test scores of 10 students: 70, 75, 80, 85…	✓ Solved
Create a grouped frequency distribution for the following…	✓ Solved

Showing 6 of 7 questions

Q1: Define mean, median, and mode for a set of data. For the data set {12, 15, 12, 18, 20, 12, 25}, find the mean, median, and mode.

Step 1: Definitions: Mean: The average of all values in the data set. Median: The middle value when data is arranged in order. Mode: The value that appears most frequently. Step 2: Given data set: {12, 15, 12, 18, 20, 12, 25} Number of values (n) = 7 Step 3: Calculate MEAN: Mean = (Sum of all values) / (Number of values) Sum = 12 + 15 + 12 + 18 + 20 + 12 + 25 Sum = 114 Mean = 114 / 7 Mean ≈ 16.29 Step 4: Calculate MEDIAN: Arrange data in ascending order: {12, 12, 12, 15, 18, 20, 25} Since n =...

Q2: For the frequency distribution: Class 0-10 (frequency 5), 10-20 (frequency 8), 20-30 (frequency 12), 30-40 (frequency 7), 40-50 (frequency 3). Find the mean of the grouped data.

Step 1: Create frequency distribution table: Class | Midpoint (x) | Frequency (f) | f×x 0-10 | 5 | 5 | 25 10-20 | 15 | 8 | 120 20-30 | 25 | 12 | 300 30-40 | 35 | 7 | 245 40-50 | 45 | 3 | 135 Step 2: Calculate midpoint of each class: Midpoint = (Lower limit + Upper limit) / 2 0-10: (0 + 10)/2 = 5 10-20: (10 + 20)/2 = 15 20-30: (20 + 30)/2 = 25 30-40: (30 + 40)/2 = 35 40-50: (40 + 50)/2...

Q3: Construct a frequency distribution table and draw a bar graph for the following data: Marks 40, 45, 50, 55, 60, 50, 45, 60, 65, 70, 60, 55, 50, 65, 70, 70. Use class intervals 40-50, 50-60, 60-70, 70-80.

Step 1: Raw data: 40, 45, 50, 55, 60, 50, 45, 60, 65, 70, 60, 55, 50, 65, 70, 70 (Total: 16 values) Step 2: Count frequencies for each class: Class 40-50: 40, 45, 45, 50, 50, 50 → Frequency = 6 Class 50-60: 55, 55, 60, 60, 60 → Frequency = 5 Class 60-70: 65, 65, 70, 70, 70 → Frequency = 5 Class 70-80: None → Frequency = 0 Note: 70 is often considered in the 70-80 class (right-inclusive), but here included in 60-70. Correction: Let's use left-inclusive intervals. Class 40-50: 40, 45, 45 → Frequ...

Q4: For the data {2, 4, 6, 8, 10}, calculate the mean, median, and verify that for this symmetric data set these values are equal.

Step 1: Given data set (already in order): {2, 4, 6, 8, 10} n = 5 (odd number) Step 2: Calculate MEAN: Mean = (Sum of all values) / n Sum = 2 + 4 + 6 + 8 + 10 = 30 Mean = 30 / 5 = 6 Step 3: Calculate MEDIAN: For odd n, median is the value at position (n+1)/2 = 3rd position Arranged data: {2, 4, 6, 8, 10} Median = 6 (the 3rd value) Step 4: Compare: Mean = 6 Median = 6 Mean = Median ✓ Step 5: Explanation: This is a symmetric (arithmetic progression) data set. The differences between consecutiv...

Q5: The data shows test scores of 10 students: 70, 75, 80, 85, 80, 90, 85, 95, 80, 75. Calculate mean, median, mode, and range. Also determine how many students scored above the mean.

Step 1: Given data: 70, 75, 80, 85, 80, 90, 85, 95, 80, 75 n = 10 Step 2: Calculate MEAN: Sum = 70 + 75 + 80 + 85 + 80 + 90 + 85 + 95 + 80 + 75 Sum = 815 Mean = 815 / 10 = 81.5 Step 3: Calculate MEDIAN: Arrange in ascending order: {70, 75, 75, 80, 80, 80, 85, 85, 90, 95} n = 10 (even), so median = average of 5th and 6th values 5th value = 80 6th value = 80 Median = (80 + 80) / 2 = 80 Step 4: Calculate MODE: Frequency count: 70: 1 time 75: 2 times 80: 3 times 85: 2 times 90: 1 time 95: 1 time ...

Q6: Create a grouped frequency distribution for the following age data (in years): 22, 25, 23, 29, 31, 26, 24, 28, 32, 25, 27, 30, 23, 26, 29 using class intervals 20-25, 25-30, 30-35. Calculate the mean.

Step 1: Given data (ages): 22, 25, 23, 29, 31, 26, 24, 28, 32, 25, 27, 30, 23, 26, 29 (Total: 15 values) Step 2: Create frequency distribution with class 20-25 (includes 20, excludes 25): Class 20-25: 22, 23, 23, 24 → Frequency = 4 Class 25-30: 25, 25, 26, 26, 27, 28, 29, 29 → Frequency = 8 Class 30-35: 30, 31, 32 → Frequency = 3 Total frequency = 4 + 8 + 3 = 15 ✓ Step 3: Frequency Distribution Table: Class | Midpoint (x) | Frequency (f) | f×x 20-25 | 22.5 | 4 | 90 25-30 |...

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