Statistics — Questions & Answers

Sample questions from Statistics

1. Q1. If each observation is increased by 4, the mean: Verify the related mean calculation:

   • A.increases by 4✓
   • B.increases by 16
   • C.does not change
   • D.decreases by 4
   Solution

   Adding a constant to every observation adds it to the mean.

2. Q2. The mean of the distribution x = 3, 5, 7, 9, 11, 13 with frequencies f = 6, 8, 15, p, 8, 4 is 7.5. The value of p is:

   • A.5
   • B.2
   • C.4
   • D.3✓
   Solution

   Σfx = 18 + 40 + 105 + 9p + 88 + 52 = 303 + 9p and Σf = 41 + p. Setting (303 + 9p)/(41 + p) = 7.5 gives 303 + 9p = 307.5 + 7.5p, so 1.5p = 4.5 and p = 3. The equation must be cleared of the fraction before solving — treating the mean as Σfx/6 ignores that the frequencies, not the number of values, form the denominator.

3. Q3. A data set has mean 12. If every value is reduced by 3, new mean is:

   • A.9✓
   • B.12
   • C.15
   • D.36
   Solution

   Subtracting 3 from every observation subtracts 3 from the mean.

4. Q4. The empirical relationship between the three measures of central tendency is

   • A.3 Mean = Mode + 2 Median
   • B.3 Mode = Mean + 2 Median
   • C.Mode = 3 Mean − 2 Median
   • D.3 Median = Mode + 2 Mean✓
   Solution

   The NCERT empirical relation is 3 Median = Mode + 2 Mean, equivalently Mode = 3 Median − 2 Mean.

5. Q5. Using the step-deviation method with a = 25 and h = 10 for the distribution 0–10: 4, 10–20: 8, 20–30: 15, 30–40: 15, 40–50: 8, the mean is

   • A.26
   • B.27
   • C.28✓
   • D.30
   Solution

   uᵢ = −2, −1, 0, 1, 2 so Σfᵢuᵢ = −8 − 8 + 0 + 15 + 16 = 15 with Σfᵢ = 50. Mean = 25 + 10 × (15/50) = 28.

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