In an experiment with 15 observations on x, the following results were available $\sum x^{2} = 2830, \sum x = 170 .$ One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

8.33

78.00

188.66

177.33

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$n = 15, \sum x = 170, \sum x^{2} = 2830$

One observation entered wrongly

20 instead of 30

$\sum x + 30 - 20 = 180$

New Mean $= X = \frac{180}{15} = 12$

$\sum X^{2} = \sum x^{2} + 30^{2} - 20^{2} = 3330$

Variance $= \frac{\sum X^{2}}{n} - {(X)}^{2}$

$= \frac{3330}{15} - 144 = 222 - 144 = 78$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE