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Model Paper 3 — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsModel Paper 34 Marks
Question
Read the text carefully and answer the questions:
Different organisations collect the data and analyse it quantitatively. During one such analysis some mistake crept in. The result given was that mean and variance of 100 observations as 40 and 5.1 but later on rechecking it was found that one observation was mistakenly taken as 50 instead of 40 .
(a) What is incorrect sum of variates?
(b) What is correct sum of observations?
(c) What is incorrect $\Sigma x^{2}$ ?
OR
What is corrected variance?
✓

Answer

(i) Mean $=40, \mathrm{n}=100$, sum $=100 \times 40=4000$
(ii) Corrected sum $=4000-50+40=3990$
(iii) $\sigma^{2}=\frac{\Sigma x^{2}}{n}-\left(\frac{\Sigma x}{n}\right)^{2}$
$\Rightarrow(5.1)^{2}=\frac{\Sigma x^{2}}{100}-(40)^{2}$
$\Rightarrow(26.01+1600) 100=\Sigma x^{2}$
OR
Corrected $\Sigma x^{2}=162601-(50)^{2}+(40)^{2}$
$=162601-2500+1600=161701$
Corrected $\sigma^{2}=\frac{161701}{100}-(39.9)^{2}$
$=1617.01-1592.01=25$
38. Read the text carefully and answer the questions:

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