# What are the Sample Variance and Sample Standard Deviation of the Following Data Set: 4, 7, 9,10,16.

We will be using the formula of sample variance and standard deviation to solve this.

## Answer: The Sample Variance and Sample Standard Deviation of the Following Data Set: 4, 7, 9, 10, 16 are 19.7 and 4.4

Let's solve this step by step.

**Explanation:**

Given that, Data set: 4, 7, 9, 10, 16.

Mean = (4 + 7 + 9 + 10 + 16) / 5 = 46/5 = 9.2

Sample Standard Deviation Formula is given by the S = √1/n−1 ∑^{n}_{i=1}(x_{i} − ¯x)^{2}

Here, ¯x = sample average, x = individual values in sample, n = count of values in the sample.

On substituting the values, we get

S = √1/n−1 ∑^{n}_{i=1}(x_{i} − ¯x)^{2}

S = √1/5−1 {(4 - 9.2)^{2} + (7 - 9.2)^{2} + (9 - 9.2)^{2} + (10 - 9.2)^{2} + (16 - 9.2)^{2}}

S = √1/4 {(-5.2)^{2} + (-2.2)^{2} + (-0.2)^{2} + (0.8)^{2} + (6.8)^{2}}

S = √1/4 {27.04 + 4.84 + 0.4 + 0.64 + 46.24}

S = √1/4 (78.8)

S = √19.7

S = 4.4

You can use Cuemath's online Standard Deviation Calculator to calculate the standard deviation of this data set.

Sample Variance is given by the formula S^{2} = 1/n−1 ∑^{n}_{i=1}(x_{i} − ¯x)^{2}

S^{2} = 19.7