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What is the mean and standard deviation of the following data set?

40.1, 41.1, 39.5, 40.1, 39.1,
41.2, 37.6, 39.1, 41.6, 40.8,
43.2, 38.9, 38.1, 43.5, 36.9,
39.1, 40.5, 41.2, 37.6, 44.0,
38.0, 39.8, 42.1, 38.6, 41.3,
43.7, 36.9, 43.6, 38.1, 40.2

Answer :

The mean of the given data set is approximately 39.78, and the standard deviation is approximately 1.571.

To find the mean and standard deviation of the given data set, we can use the following steps:

Calculate the mean:

Add up all the values in the data set and divide the sum by the total number of values.

Mean = (40.1 + 41.1 + 39.5 + 40.1 + 39.1 + 41.2 + 37.6 + 39.1 + 41.6 + 40.8

+ 43.2 + 38.9 + 38.1 + 43.5 + 36.9 + 39.1 + 40.5 + 41.2 + 37.6

+ 44.0 + 38.0 + 39.8 + 42.1 + 38.6 + 41.3 + 43.7 + 36.9 + 43.6

+ 38.1 + 40.2) / 30

Mean = 39.78 (rounded to two decimal places)

Calculate the standard deviation:

Subtract the mean from each value, square the result, sum up the squared differences, divide by the total number of values, and take the square root.

Standard deviation = √[( (40.1 - 39.78)^2 + (41.1 - 39.78)^2 + (39.5 - 39.78)^2 + ... + (40.2 - 39.78)^2 ) / 30]

Standard deviation = 1.571 (rounded to three decimal places)

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