Question

In an experiment with 15 observations on x the following results were available ∑xi² = 2830, ∑xi = 170, on observation that was 20 was found to be wrong and was replaced by the correct value of 30 then the corrected variance is

(a) 80.33

(b) 188.66

(c) 78

(d) 177.33

Answer 1

The correct option  (c) 78

Explanation:

∑xi² = 2830

∑xi = 170

Observation value 20 is replaced by 30.

∴ ∑xi' = 170 – 20 + 30 = 180

Increase in ∑xi² = 900 – 400 = 500 

hence ∑(xi²)' = 2830 + 50 = 3330.

Variance  = (1/n) ∑(xi²) – [(1/n) ∑xi']²

= (1/15)(3330) – [(1/15) × 180]²

= 222 – 144

= 78.