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= √1/n-1 ∑ⁿᵢ₌₁ (xᵢ-x)²
a.) 1.87
b.) 2.12
c.) 1.37
d.) 3.51

Answer 1

To find the standard deviation of a data set with a mean of 4, we calculate the deviations from the mean, square them, average these squares, and then take the square root of that average. The standard deviation for the data set 2, 3, 4, 4, 7 is a) 1.87.

Step-by-step explanation:

To calculate the standard deviation of the given data set (2, 3, 4, 4, 7) with a mean of 4, we'll follow these steps:

1. Subtract the mean from each data point to find the deviations: (2-4), (3-4), (4-4), (4-4), (7-4) resulting in: -2, -1, 0, 0, 3.
2. Square each deviation: (-2)^2, (-1)^2, 0^2, 0^2, 3^2 which equals: 4, 1, 0, 0, 9.
3. Sum the squared deviations: 4+1+0+0+9 = 14.
4. Divide by the number of data points minus one, also known as degrees of freedom (n-1): since there are 5 data points, degrees of freedom is 4, so we get 14/4 = 3.5. This is the variance.
5. Take the square root of the variance to find the sample standard deviation: √3.5 = 1.87 (after rounding to two decimal places).

Hence, the correct option for the standard deviation of the given data set, rounded to the hundredths place, is a.) 1.87.