Statistics — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Statistics" — 8 important questions with detailed answers for CBSE board exam preparation.
✓ 100% Free
✓ No Login Needed
✓ NCERT / CBSE Aligned
✓ Download as PDF
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Statistics" — 8 important questions with detailed answers for CBSE board exam prep…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
🤖 Stuck on any question? Ask Syllab's free AI Tutor for a step-by-step explanation — instant, unlimited, no login.
Key Questions Covered:
- Find the mean of the data: 10, 15, 20, 25, 30
- Find the median of the data: 7, 11, 9, 15, 13, 8, 20
- Find the mode of the data: 5, 8, 5, 9, 8, 5, 7, 8, 9, 5
- Calculate the standard deviation of the data: 2, 4, 6, 8, 10
- Find the range and interquartile range of the data: 10, 12, 15, 18, 20, 25, 2…
- For the grouped data with class intervals and frequencies, find the mean. Cla…
- + 2 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the mean of the data: 10, 15, 20, 25, 30 | ✓ Solved |
| Find the median of the data: 7, 11, 9, 15, 13, 8, 20 | ✓ Solved |
| Find the mode of the data: 5, 8, 5, 9, 8, 5, 7, 8, 9, 5 | ✓ Solved |
| Calculate the standard deviation of the data: 2, 4, 6, 8, 10 | ✓ Solved |
| Find the range and interquartile range of the data: 10, 1… | ✓ Solved |
| For the grouped data with class intervals and frequencies… | ✓ Solved |
Showing 6 of 8 questions
Q1: Find the mean of the data: 10, 15, 20, 25, 30
Given data: 10, 15, 20, 25, 30
Step 1: Use the formula for mean:
Mean = (Sum of all observations)/(Number of observations)
Step 2: Calculate the sum:
Sum = 10 + 15 + 20 + 25 + 30 = 100
Step 3: Count the number of observations:
N = 5
Step 4: Calculate the mean:
Mean = 100/5 = 20
Final Answer: The mean is 20
Q2: Find the median of the data: 7, 11, 9, 15, 13, 8, 20
Given data: 7, 11, 9, 15, 13, 8, 20
Step 1: Arrange the data in ascending order:
7, 8, 9, 11, 13, 15, 20
Step 2: Count the number of observations:
N = 7 (odd number)
Step 3: For odd n, median is the middle value:
Median is at position (n + 1)/2 = (7 + 1)/2 = 4
Step 4: The 4th value in the ordered list:
Median = 11
Final Answer: The median is 11
Q3: Find the mode of the data: 5, 8, 5, 9, 8, 5, 7, 8, 9, 5
Given data: 5, 8, 5, 9, 8, 5, 7, 8, 9, 5
Step 1: Count the frequency of each value:
5 appears 4 times
8 appears 3 times
9 appears 2 times
7 appears 1 time
Step 2: Identify the value with maximum frequency:
The value 5 appears most frequently (4 times).
Step 3: The mode is the value with the highest frequency:
Mode = 5
Final Answer: The mode is 5
Q4: Calculate the standard deviation of the data: 2, 4, 6, 8, 10
Given data: 2, 4, 6, 8, 10
Step 1: Calculate the mean:
Mean = (2 + 4 + 6 + 8 + 10)/5 = 30/5 = 6
Step 2: Find deviations from mean:
(2 - 6) = -4
(4 - 6) = -2
(6 - 6) = 0
(8 - 6) = 2
(10 - 6) = 4
Step 3: Square the deviations:
(-4)² = 16
(-2)² = 4
(0)² = 0
(2)² = 4
(4)² = 16
Step 4: Find the variance:
Variance = (16 + 4 + 0 + 4 + 16)/5 = 40/5 = 8
Step 5: Find the standard deviation:
Standard Deviation = √Variance = √8 = 2√2
Final Answer: Standard deviation = 2√2 ≈ 2.83
Q5: Find the range and interquartile range of the data: 10, 12, 15, 18, 20, 25, 28, 32
Given data: 10, 12, 15, 18, 20, 25, 28, 32 (already sorted)
Step 1: Find the range:
Range = Maximum value - Minimum value
Range = 32 - 10 = 22
Step 2: Find Q1 (first quartile):
N = 8 (even number)
Q1 is the median of the lower half: 10, 12, 15, 18
Q1 = (12 + 15)/2 = 27/2 = 13.5
Step 3: Find Q3 (third quartile):
Q3 is the median of the upper half: 20, 25, 28, 32
Q3 = (25 + 28)/2 = 53/2 = 26.5
Step 4: Find the interquartile range (IQR):
IQR = Q3 - Q1 = 26.5 - 13.5 = 13
Final Answer: Range = 2...
Q6: For the grouped data with class intervals and frequencies, find the mean. Classes: 0-10, 10-20, 20-30, 30-40 with frequencies 5, 8, 12, 5 respectively.
Given grouped data:
Class intervals: 0-10, 10-20, 20-30, 30-40
Frequencies: 5, 8, 12, 5
Step 1: Find the class marks (midpoints):
Class marks: 5, 15, 25, 35
Step 2: Create the frequency table:
Class f x fx
0-10 5 5 25
10-20 8 15 120
20-30 12 25 300
30-40 5 35 175
Total 30 620
Step 3: Use the formula for grouped data mean:
Mean = Σ(fx)/Σf
Step 4: Calculate:
Mean = 620/30 = 62/3 ≈ 20.67
Final Answer: The mean is 62/3 or approximately 20.67
Showing 6 of 8 questions. Visit the full page for complete solutions.
More Class 11 Mathematics NCERT Solutions
- Sets — Class 11 Mathematics NCERT Solutions
- Relations and Functions — Class 11 Mathematics NCERT Solutions
- Trigonometric Functions — Class 11 Mathematics NCERT Solutions
- Complex Numbers and Quadratic Equations — Class 11 Mathematics NCERT Solutions
- Linear Inequalities — Class 11 Mathematics NCERT Solutions
- Permutations and Combinations — Class 11 Mathematics NCERT Solutions
- Binomial Theorem — Class 11 Mathematics NCERT Solutions
- Sequences and Series — Class 11 Mathematics NCERT Solutions
- Straight Lines — Class 11 Mathematics NCERT Solutions
- Conic Sections — Class 11 Mathematics NCERT Solutions
- Introduction to Three Dimensional Geometry — Class 11 Mathematics NCERT Solutions
- Limits and Derivatives — Class 11 Mathematics NCERT Solutions
- Probability — Class 11 Mathematics NCERT Solutions
- Sets Exemplar — Class 11 Mathematics NCERT Solutions