If the variance of the data 2,3,5,8,12 is σ^2 and the mean deviation from the median for this data is M , then σ^2-M=

Correct answer: A. 10.2 Observations : 2,3,5,8,12 Mean =(2+3+5+8+12)/(5)=6 σ^2=13.2 Median =5=m Mean deviation about median ( |x_i-m|)/(n)=(3+2+0+3+7)/(5)=3M=3 σ^2-M=13.2-3=10.2

BITSAT 2024Paper 2

Exam: BITSAT
Year: 2024
Paper: Paper 2
Subject: Mathematics
Chapter: Statistics

BITSAT 2024 · Paper 2 · Mathematics · Statistics

If the variance of the data 2,3,5,8,12 is σ^2 and the mean...

If the variance of the data

2,3,5,8,12

\sigma^2

and the mean deviation from the median for this data is M , then

\sigma^2-\mathrm{M}=

Options

A $10.2$
B $5.8$
C $10.6$
D $8.2$

Correct answer

A. $10.2$

Step-by-step solution

Observations :

2,3,5,8,12

Mean

=\frac{2+3+5+8+12}{5}=6\therefore \sigma^2=13.2

Median

=5=m\therefore \quad

Mean deviation about median

\Rightarrow \quad \frac{\Sigma\left|x_i-m\right|}{n}=\frac{3+2+0+3+7}{5}=3M=3 \Rightarrow \sigma^2-M=13.2-3=10.2

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