Given the following sample data: 18, 21, 32, 41
1) Calculate the sample variance. Keep to 2 decimal places.
2) Determine the sample standard deviation. Keep to two decimal places

Solution:

Given, the sample data is 18, 21, 32, 41.

1) we have to find the sample variance.

The sample variance can be calculated using the formula

\(\sigma ^{2}=\frac{\sum (X-\mu )^{2}}{n-1}[/latex]

Here, X = sample data

μ = mean

n = number of terms in the sample data.

Mean = (18 + 21 + 32 + 41)/4 = 112/4 = 28

\(\\\sigma ^{2}=\frac{(18-28)^{2}+(21-28)^{2}+(32-28)^{2}+(41-28)^{2}}{4-1} \\=\frac{(-10)^{2}+(-7)^{2}+(4)^{2}+(13)^{2}}{3} \\=\frac{100+49+16+169}{3} \\=\frac{334}{3}\)

= 111.333

Therefore, the variance is 111.333.

2) We have to find the standard deviation.

Standard deviation = square root of the variance

So, standard deviation = √111.333

= 10.551

Therefore, the standard deviation is 9.14.

Therefore,

1) The sample variance up to 2 decimal places is 111.333

2) The sample standard deviation up to two decimal places is 10.551