Variance of the numbers 3, 7, 10,18, 22 is equal to?
The variance (in statistics and probability theory) of a random variable, probability distribution, or sample is a measure of the statistical dispersion of possible values around the expected value, and is equal to the expected value (or mean) squared of the deviations of the possible values from the expected value (or mean). That is, while the expected value describes the mean location of a particular distribution, the variance describes the extent to which the possible values of that distribution are spread around the expected value. The positive square root of the variance is called the standard deviation, and it has the same units as the original data, so it is sometimes easier to understand or interpret compared to the variance.
Variance of the numbers 3, 7, 10,18, 22 is equal to?
D49.2
The mean of the given items
x
ˉ
=
5
3+7+10+18+22
=12
Hence, variance =
n
1
∑(xX
i
−
x
ˉ
)X
2
=
5
1
{(3−12)
2
+(7−12)
2
+(10−12)
2
+(18−12)
2
+(22−12)
2
}
=
5
1
{81+25+4+36+100}=
5
246
=49.2