Class 11 • Maths • Chapter 13
STATISTICS
True & False Quiz
Measure. Disperse. Analyse.
✓True
✗False
25
Questions
|
Ch.13
Chapter
|
XI
Class
Why True & False for STATISTICS?
How this format sharpens your conceptual clarity
🔵 Statistics is the science of uncertainty and data — used in medicine, economics, and every field that collects information.
✅ T/F targets measures of dispersion (variance, SD, MD) — concepts students confuse, making these high-scoring discrimination questions.
🎯 Variance is NEVER negative (sum of squares); adding a constant to all data does NOT change variance.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The arithmetic mean of \(5,7,9\) is \(7\).
Q 2
If all observations are equal, their variance is zero.
Q 3
The mean of grouped data depends on class midpoints.
Q 4
The sum of deviations from the arithmetic mean is always zero.
Q 5
Mean deviation is always non-negative.
Q 6
Median is affected more by extreme values than mean.
Q 7
The mode of a symmetric unimodal distribution equals its mean.
Q 8
Class width is the difference between successive class limits.
Q 9
Cumulative frequency can be “less than” or “more than”.
Q 10
The variance has the same unit as the data.
Q 11
Standard deviation is the square root of variance.
Q 12
Mean deviation about mean is always less than or equal to standard deviation.
Q 13
If each observation is multiplied by \(k\), variance becomes \(k^2\) times.
Q 14
Adding a constant to every observation changes the variance.
Q 15
Step deviation method simplifies mean computation for large data.
Q 16
For continuous data, median is found using class boundaries.
Q 17
The empirical relation \( \text{Mode}=3\text{Median}-2\text{Mean} \) always holds.
Q 18
Range considers only the smallest and largest observations.
Q 19
Coefficient of variation is unit-free.
Q 20
Two datasets with equal mean must have equal standard deviation.
Q 21
If frequencies are doubled, standard deviation also doubles.
Q 22
For a frequency distribution, \(\sum f(x-\bar x)=0\).
Q 23
Among datasets with same mean, the one with larger variance is more dispersed.
Q 24
If \(X\) has variance \(\sigma^2\), then \(Y=aX+b\) has variance \(a^2\sigma^2\).
Q 25
Minimum variance of a dataset occurs when all observations are equal.
Key Takeaways — STATISTICS
Core facts for CBSE Boards & JEE
1
Variance = Σ(xᵢ−x̄)²/n — always non-negative; SD = √Variance.
2
Adding constant k: mean increases by k, variance UNCHANGED.
3
Multiplying by k: mean multiplied by k, variance multiplied by k².
4
Mean Deviation is MINIMUM when calculated about the median.
5
CV = (σ/x̄)×100 — used to compare variability of two series.
6
Symmetric distribution: Mean = Median = Mode.