Question

Calculate the standard deviation of a given data set using the standard deviation formula or excel. consider the following data set that has a mean of 4: 2, 3, 4, 4, 7 using the equation below or the standard deviation formula in excel, calculate the standard deviation for this data set. answer choices are rounded to the hundredths place. s equals square root of fraction numerator 1 over denominator n minus 1 end fraction sum from i equals 1 to n of open parentheses x subscript i minus x with bar on top close parentheses squared end root.

Calculate the standard deviation for the given data set.
A) 1.87
B) 2.12
C) 1.37
D) 3.51

Answer 1

To calculate the standard deviation, find the variance of the data set by finding the average of the squared deviations from the mean. Then, take the square root of the variance. For this data set, the standard deviation is approximately 1.87.

Step-by-step explanation:

To calculate the standard deviation, we first need to find the variance. The variance is the average of the squared deviations of each data point from the mean. Let's calculate the variance step-by-step:

1. Find the deviation of each data point from the mean:
   2 - 4 = -2
   3 - 4 = -1
   4 - 4 = 0
   4 - 4 = 0
   7 - 4 = 3
2. Square each deviation:
   (-2)^2 = 4
   (-1)^2 = 1
   0^2 = 0
   0^2 = 0
   3^2 = 9
3. Sum up all the squared deviations:
   4 + 1 + 0 + 0 + 9 = 14
4. Divide the sum by n-1, where n is the number of data points:
   14 / (5-1) = 14 / 4 = 3.5

Next, we find the square root of the variance to get the standard deviation:
sqrt(3.5) ≈ 1.87

So, the standard deviation for this data set is approximately 1.87.