Statistics — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Statistics" — 9 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Statistics" — 9 important questions with detailed answers for CBSE board exam prep…

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

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Key Questions Covered:

Find the mean of the following grouped data using the assumed mean method: Cl…
Find the median of the following grouped data: Class Interval: 0-5, 5-10, 10-…
Find the mode of the following grouped data: Class Interval: 10-20, 20-30, 30…
The mean of the following grouped data is 24. Find the missing frequency f: C…
Draw an ogive for the following cumulative frequency distribution and find th…
Find the mean deviation about the mean for the following grouped data: Class …
+ 3 more questions in the full chapter

Solutions Summary:

Question	Status
Find the mean of the following grouped data using the ass…	✓ Solved
Find the median of the following grouped data: Class Inte…	✓ Solved
Find the mode of the following grouped data: Class Interv…	✓ Solved
The mean of the following grouped data is 24. Find the mi…	✓ Solved
Draw an ogive for the following cumulative frequency dist…	✓ Solved
Find the mean deviation about the mean for the following …	✓ Solved

Showing 6 of 9 questions

Q1: Find the mean of the following grouped data using the assumed mean method: Class Interval: 0-10, 10-20, 20-30, 30-40, 40-50 Frequency: 5, 15, 20, 8, 2

Step 1: Construct the table with class midpoints (x) and deviations (d) from assumed mean 25 Step 2: Assumed mean A = 25 (midpoint of 20-30) Step 3: Class Intervals and calculations: 0-10: midpoint = 5, d = 5-25 = -20, f = 5, fd = -100 10-20: midpoint = 15, d = 15-25 = -10, f = 15, fd = -150 20-30: midpoint = 25, d = 25-25 = 0, f = 20, fd = 0 30-40: midpoint = 35, d = 35-25 = 10, f = 8, fd = 80 40-50: midpoint = 45, d = 45-25 = 20, f = 2, fd = 40 Step 4: Sum of frequenci...

Q2: Find the median of the following grouped data: Class Interval: 0-5, 5-10, 10-15, 15-20, 20-25 Frequency: 4, 6, 12, 8, 5

Step 1: Find cumulative frequencies 0-5: f = 4, cf = 4 5-10: f = 6, cf = 10 10-15: f = 12, cf = 22 15-20: f = 8, cf = 30 20-25: f = 5, cf = 35 Step 2: Total frequency N = 35 Step 3: N/2 = 35/2 = 17.5 Step 4: Median class is 10-15 (since cf = 22 is just greater than 17.5) Step 5: Median = L + [(N/2 - cf)/f] × h Step 6: Here, L = 10 (lower limit of median class), N/2 = 17.5 Step 7: cf = 10 (cumulative frequency before median class) Step 8: f = 12 (frequency of median class...

Q3: Find the mode of the following grouped data: Class Interval: 10-20, 20-30, 30-40, 40-50, 50-60 Frequency: 3, 7, 12, 8, 5

Step 1: The modal class is the class with the highest frequency Step 2: Frequencies: 3, 7, 12, 8, 5 Step 3: Modal class is 30-40 (frequency = 12) Step 4: Mode = L + [(f1 - f0)/(2f1 - f0 - f2)] × h Step 5: Here, L = 30 (lower limit of modal class) Step 6: f1 = 12 (frequency of modal class) Step 7: f0 = 7 (frequency of class before modal class) Step 8: f2 = 8 (frequency of class after modal class) Step 9: h = 10 (class width) Step 10: Mode = 30 + [(12 - 7)/(2(12) - 7 - 8)] × 10 Step 11: Mode = 30 ...

Q4: The mean of the following grouped data is 24. Find the missing frequency f: Class Interval: 10-15, 15-20, 20-25, 25-30, 30-35 Frequency: 4, 6, f, 8, 2

Step 1: Set up table with class midpoints 10-15: x = 12.5, f = 4, fx = 50 15-20: x = 17.5, f = 6, fx = 105 20-25: x = 22.5, f = f, fx = 22.5f 25-30: x = 27.5, f = 8, fx = 220 30-35: x = 32.5, f = 2, fx = 65 Step 2: Total frequency = 4 + 6 + f + 8 + 2 = 20 + f Step 3: Sum of fx = 50 + 105 + 22.5f + 220 + 65 = 440 + 22.5f Step 4: Mean formula: Mean = Σfx/Σf Step 5: 24 = (440 + 22.5f)/(20 + f) Step 6: 24(20 + f) = 440 + 22.5f Step 7: 480 + 24f = 440 + 22.5f Step 8: 24f - 22...

Q5: Draw an ogive for the following cumulative frequency distribution and find the median graphically: Class Interval: 0-10, 10-20, 20-30, 30-40, 40-50 Cumulative Frequency: 8, 20, 35, 48, 50

Step 1: For an ogive, plot the upper class limits on x-axis and cumulative frequencies on y-axis Step 2: Points to plot: (10, 8), (20, 20), (30, 35), (40, 48), (50, 50) Step 3: Draw a smooth curve through these points Step 4: To find median graphically: Find N/2 = 50/2 = 25 on y-axis Step 5: From point (0, 25), draw a horizontal line to meet the ogive Step 6: From the intersection point, draw a perpendicular to x-axis Step 7: The point where it meets x-axis gives the median Step 8: From the plot...

Q6: Find the mean deviation about the mean for the following grouped data: Class Interval: 0-10, 10-20, 20-30, 30-40 Frequency: 5, 8, 12, 5

Step 1: Find the mean first Step 2: Midpoints: 5, 15, 25, 35 Step 3: fx values: 5×5=25, 8×15=120, 12×25=300, 5×35=175 Step 4: Σf = 5 + 8 + 12 + 5 = 30 Step 5: Σfx = 25 + 120 + 300 + 175 = 620 Step 6: Mean = 620/30 = 20.67 Step 7: Find deviations from mean: |x - mean| Class 0-10: |5 - 20.67| = 15.67, f|x-mean| = 5 × 15.67 = 78.35 Class 10-20: |15 - 20.67| = 5.67, f|x-mean| = 8 × 5.67 = 45.36 Class 20-30: |25 - 20.67| = 4.33, f|x-mean| = 12 × 4.33 = 51.96 Class 30-40: |35 - 20....

Showing 6 of 9 questions. Visit the full page for complete solutions.