Question

Calculate the standard deviation and variance of the given random sample data. Round to two decimal places.

X
18.4
19.4
16.7
28.2
3.5
Find the variance and standard Deviation. Round your answer to one decimal place.
x 0 1 2 3 4
P(X = x) 0.1 0.2 0.2 0.3 0.2

Answer 1

Variance ≈ 63.1

Standard Deviation ≈ 7.9

Therefore, the variance is approximately 63.1 and the standard deviation is approximately 7.9.

Explanation:

To calculate the variance and standard deviation for the given random sample data, we'll follow these steps:

Calculate the mean of the data.

Calculate the squared difference between each data point and the mean.

Calculate the variance by taking the average of the squared differences.

Calculate the standard deviation by taking the square root of the variance.

Let's perform the calculations:

Calculate the mean:

Mean = (18.4 + 19.4 + 16.7 + 28.2 + 3.5) / 5

Mean = 17.24

Calculate the squared difference between each data point and the mean:

(18.4 - 17.24)² = 1.34² = 1.7956

(19.4 - 17.24)² = 2.16² = 4.6656

(16.7 - 17.24)² = (-0.54)² = 0.2916

(28.2 - 17.24)² = 10.96² = 120.2416

(3.5 - 17.24)² = (-13.74)² = 188.5476

Calculate the variance:

Variance = (1.7956 + 4.6656 + 0.2916 + 120.2416 + 188.5476) / 5

Variance ≈ 63.10

Calculate the standard deviation:

Standard Deviation ≈ √63.10

Standard Deviation ≈ 7.95

Rounding to one decimal place:

Variance ≈ 63.1

Standard Deviation ≈ 7.9

Therefore, the variance is approximately 63.1 and the standard deviation is approximately 7.9.