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26/12/2021 1:01 pm
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Mean & standard deviation of 20 observations are 10 & 2.5. It is observed that are entry was taken 25 instead of 35. Find correct means & variance.
(a) 10.5, 26
(b) 10.5, 25
(c) 11, 26
(d) 11, 25
1 Answer
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26/12/2021 1:18 pm
Answer (a) 10.5, 26
Explanation
n = 20, \(\bar{x}\) = 10, σ = 2.5
\(\bar{x_{new}}\) = \(\frac{20 \bar{x} - 25 + 35}{20}\)
= 10.5
2.5 = \(\sqrt{\frac{\sum x_i^2}{n} - (\bar x)^2}\)
Σxi2 = 2125
∴ (Σxi2)new = 2125 - 625 + 1225
= 2725
∴ σnew = \(\sqrt{\frac{2725}{20} - (10.5)^2}\)
= 26
This post was modified 3 years ago by admin