Question

Use the following data set to find the standard deviation of the set. 46, 34, 25, 31, 15, 50, 37, 42

Answer 1

The given data exists 46, 34, 25, 31, 15, 50, 37, 42

Mean, μ = 35

Variance, σ² = 114.5

Standard deviation, σ = 10.7004

What is the standard deviation?

A standard deviation (or σ) exists as a measure of how dispersed the data exists concerning the mean. Low standard deviation indicates data exist clustered about the mean, and high standard deviation suggests data exist better spread out.

Given data 46, 34, 25, 31, 15, 50, 37, 42

The number of elements exists n = 8 (8 numbers in the set)

To calculate the mean,

(46+34+25+31+15+50+37+42)/8 = 280/8 = 35

μ = 35

To calculate the variance,

Sum of the squared difference between each number of the set and the mean divided by the number of elements of the sample minus one.

Variance = [(46-35)² + (34-35)² + (25-35)² + (31-35)² + (15-35)²+ (50-35)² + (37-35)² + (42-35)²]/8

= 916/8

= 114.5

σ² = 114.5

Standard deviation exists as the square root of the variance.

σ² = 114.5

√σ² = √114.5

σ = 10.7004

Therefore, the standard deviation exists at 10.70.

To learn more about standard deviation  refer to:

brainly.com/question/14586559

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