Statistics — Class 11 MCQs with Answers

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

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

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

   A4B5C7D6
   Show answerHide answer

   Answer: 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. Q2 of 6Easy

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

   A7B9C2D5
   Show answerHide answer

   Answer: 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. Q3 of 6Medium

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

   AcBOriginal meanCOriginal mean + cDOriginal mean × c
   Show answerHide answer

   Answer: 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.

4. Q4 of 6Medium

   Assertion (A): The mean deviation about the mean of 3, 5, 9, 11 and 12 is 3.2. Reason (R): M.D.(x̄) = (1/n) Σ|xᵢ – x̄|, the mean of the absolute deviations from the mean.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
   Show answerHide answer

   Answer: Both A and R are true and R is the correct explanation of A

   Explanation: A is true: the mean is 40/5 = 8, the absolute deviations are 5, 3, 1, 3, 4 with sum 16, and 16/5 = 3.2. R is the formula used to get this value, so R explains A.

5. Q5 of 6Hard

   Mean deviation about median of {2, 4, 6, 8, 10, 12, 14}:

   A6B3C5D24/7 ≈ 3.43
   Show answerHide answer

   Answer: 24/7 ≈ 3.43

   Explanation: Median is 8; absolute deviations |2−8| through |14−8| are 6,4,2,0,2,4,6, summing to 24. Dividing by n=7 gives mean deviation 24/7 ≈ 3.43 — leaving the sum undivided, 24, is the usual shortcut error.

6. Q6 of 6Hard

   Assertion (A): The mean and variance of four observations are 5 and 5. If two of the observations are 2 and 4, the other two are 6 and 8. Reason (R): Adding the same constant to every observation does not change the variance.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
   Show answerHide answer

   Answer: Both A and R are true but R is not the correct explanation of A

   Explanation: A is true: x + y = 20 – 6 = 14 and Σxᵢ² = 4(5 + 25) = 120, so x² + y² = 120 – 4 – 16 = 100, giving xy = 48 and x, y = 6, 8. R is also true, but it plays no part in finding the two observations.

Statistics notes: key concepts (Class 11 Mathematics)

Two data sets can share a mean yet differ wildly in spread. This chapter measures that spread: the range, the mean deviation about the mean or median, the variance and its square root the standard deviation, and the coefficient of variation, which compares consistency across data measured on different scales.

Measures of dispersion

They quantify how scattered data is about a central value; range, mean deviation, variance and standard deviation are the four studied here.

Range

The simplest measure: maximum value minus minimum value. It uses only the two extremes, so it ignores how the middle data is spread.

Mean deviation about the mean

The average of the absolute distances of observations from the mean; absolute values are taken so positive and negative deviations don't cancel.

Mean deviation about the median

The average absolute deviation measured from the median; for any data set the mean deviation is least when taken about the median.

Variance

The mean of the squared deviations from the mean, denoted σ²; squaring removes signs and weights larger deviations more heavily.

Standard deviation

The positive square root of the variance, σ; it returns the spread to the original units of the data, unlike the variance.

Shortcut formula

Variance also equals the mean of the squares minus the square of the mean: σ² = (Σxᵢ²)/n − x̄², which is faster for hand computation.

Variance of grouped data

For a frequency distribution weight each squared deviation by its frequency: σ² = (1/N)Σfᵢ(xᵢ − x̄)², where N = Σfᵢ.

Effect of change of origin

Adding a constant to every observation shifts the mean but leaves the variance and standard deviation unchanged — dispersion is origin-free.

Effect of change of scale

Multiplying every observation by k multiplies the standard deviation by |k| and the variance by k²; scaling stretches the spread.

Coefficient of variation

CV = (σ/x̄)×100 expresses the spread as a percentage of the mean, giving a unit-free measure for comparing different data sets.

Comparing consistency

Between two data sets, the one with the smaller coefficient of variation is more consistent, i.e. less variable and hence more reliable.