Statistics — Class 11 MCQs with Answers

Statistics — important questions & MCQs with answers (Class 11 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Mean of 2,4,6,8,10:

   A.4

   B.5

   C.7

   D.6✓ Correct

   Answer: D. 6

   Explanation: Mean is the sum of values divided by their count: (2+4+6+8+10)/5 = 30/5 = 6. Stopping at the sum, 30, without dividing by the number of terms is what produces a wrong smaller option.

2. Q2Easy

   Range of 3,7,5,9,2:

   A.7✓ Correct

   B.9

   C.2

   D.5

   Answer: A. 7

   Explanation: Range is the spread from smallest to largest: max − min = 9 − 2 = 7. Picking the largest value alone, or subtracting in the wrong order, gives a meaningless spread.

3. Q3Easy

   Arithmetic mean of n observations is:

   A.Sum + n

   B.Sum × n

   C.Sum of observations / n✓ Correct

   D.Sum / 2

   Answer: C. Sum of observations / n

   Explanation: Arithmetic mean is total value shared equally: sum of all observations divided by n. Multiplying by n, or dividing by a fixed 2 instead of the actual count, gives a wrong average.

4. Q4Easy

   Median is the:

   A.Maximum

   B.Most frequent value

   C.Average

   D.Middle value when data is arranged✓ Correct

   Answer: D. Middle value when data is arranged

   Explanation: Median is the middle value once data is sorted in order — not simply an average of all values, nor the most frequent one, which is what mode measures instead.

5. Q5Easy

   Mode is the:

   A.Middle value

   B.Most frequent value✓ Correct

   C.Sum of all values

   D.Maximum

   Answer: B. Most frequent value

   Explanation: Mode is the value that occurs most often in the data — distinct from the middle value (median) or the total of all values, which mode has nothing to do with.

6. Q6Easy

   Range of data is:

   A.Maximum − Minimum✓ Correct

   B.Maximum + Minimum

   C.Maximum × Minimum

   D.Sum

   Answer: A. Maximum − Minimum

   Explanation: Range measures total spread as maximum minus minimum. Adding the extremes instead of subtracting, or multiplying them, produces a number with no meaning as a spread.

7. Q7Medium

   Variance is the:

   A.Average of squared deviations from mean✓ Correct

   B.Range squared

   C.Mean × median

   D.Square of mean

   Answer: A. Average of squared deviations from mean

   Explanation: Variance is the mean of the squared deviations from the mean, σ² = Σ(xᵢ−x̄)²/n — not the range squared or the mean times median, which ignore how far each value sits from x̄.

8. Q8Medium

   If a constant c is added to each observation, new mean is:

   A.c

   B.Original mean

   C.Original mean + c✓ Correct

   D.Original mean × c

   Answer: C. Original mean + c

   Explanation: Shifting every observation by a constant c shifts the mean by the same amount: new mean = original mean + c. The mean does not become just c, nor does it stay unchanged.

9. Q9Medium

   Median of {1, 2, 4, 6, 8, 10, 12, 14, 16, 18}:

   A.12

   B.8

   C.10

   D.9✓ Correct

   Answer: D. 9

   Explanation: Ten values means the median is the average of the 5th and 6th terms: sorted, these are 8 and 10, so median = (8+10)/2 = 9 — not either middle value taken alone.

10. Q10Medium

    For grouped data, mean deviation about mean =

    A.Σ f_i x_i / n

    B.Σ |x_i|/n

    C.Σ f_i |x_i − x̄|/Σ f_i✓ Correct

    D.Σ f_i (x_i − x̄)²

    Answer: C. Σ f_i |x_i − x̄|/Σ f_i

    Explanation: For grouped data, mean deviation about the mean weights each deviation by its frequency: Σfᵢ|xᵢ−x̄|/Σfᵢ. Leaving out the frequency weights, as in Σ|xᵢ|/n, ignores how often each value occurs.

11. Q11Medium

    Variance of {2, 4, 6, 8, 10}:

    A.2.83

    B.8✓ Correct

    C.16

    D.12

    Answer: B. 8

    Explanation: Mean is 6; squared deviations are 16,4,0,4,16, summing to 40. Variance = 40/5 = 8 — stopping at the sum 40 without dividing by n=5 is what produces the wrong larger option.

12. Q12Hard

    Mean deviation about mean uses:

    A.Squared deviations

    B.Absolute deviations |xᵢ−x̄|✓ Correct

    C.Cubed deviations

    D.Differences from median only

    Answer: B. Absolute deviations |xᵢ−x̄|

    Explanation: Mean deviation about the mean averages the absolute deviations, Σ|xᵢ−x̄|/n — using squared deviations instead gives variance, a different statistic that overweights values far from x̄.

13. Q13Hard

    Coefficient of Variation =

    A.mean−σ

    B.(mean/σ)×100

    C.σ²/mean

    D.(σ/mean)×100✓ Correct

    Answer: D. (σ/mean)×100

    Explanation: Coefficient of variation is spread relative to size: CV = (σ/mean) × 100. Flipping the ratio to mean/σ, or dropping the ×100, is the usual mix-up when comparing data in different units.

14. Q14Hard

    Means of groups of size 30 and 60 are 35 and 40. Combined mean:

    A.35

    B.37.5

    C.40

    D.38.33✓ Correct

    Answer: D. 38.33

    Explanation: Combined mean is size-weighted: (30×35 + 60×40)/(30+60) = (1050+2400)/90 = 3450/90 ≈ 38.33 — plain-averaging 35 and 40 to get 37.5 ignores that the second group has twice the observations.

Statistics — FAQs

More Class 11 Mathematics chapters

• 01Sets
• 02Relations and Functions
• 03Trigonometric Functions
• 04Principle of Mathematical Induction
• 05Complex Numbers and Quadratic Equations
• 06Linear Inequalities

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• Class 11 Biology chapters
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