Question:
The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :
The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :
Updated On: Feb 14, 2025
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The Correct Option is A
Solution and Explanation
$\bar{x}=\frac{2+4+10+12+14+x+y}{7}=8$
$x+y=14\dots$ (i)
$(\sigma)^{2}=\frac{\sum\left( x _{ i }\right)^{2}}{ n }-\left(\frac{\sum x _{ i }}{ n }\right)^{2}$
$16=\frac{4+16+100+144+196+ x ^{2}+ y ^{2}}{7}-8^{2}$
$16+64=\frac{460+x^{2}+y^{2}}{7}$
$560=460+x^{2}+y^{2}$
$x^{2}+y^{2}=100\dots$(ii)
Clearly by (i) and (ii), $|x-y|=2$
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Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution