Question

What is the standard deviation of the data set? 1, 4, 2, 2, 8, 7, 3 Round your answer to the nearest tenth.

Answer 1

Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.

How to calculate the standard deviation of a data set?

Step 1: Find the mean

Step 2: Find each score’s deviation from the mean

Step 3: Square each deviation from the mean

Step 4: Find the sum of squares

Step 5: Apply the formula

$SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}$

The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.

Step 1: Find the mean

The mean of the given data set can be written as,

$Mean, \mu=\dfrac{1+4+2+2+8+7+3}{7} = 3.857$

Step 2: Find each score’s deviation from the mean

1 - 3.857 = -2.857

4 - 3.857 = 0.143

2 - 3.857= -1.857

2 - 3.857= -1.857

8 - 3.857 = 4.143

7 - 3.857 = 3.143

3 - 3.857 = -0.857

Step 3: Square each deviation from the mean

-2.857² = 8.162

0.143² = 0.02

-1.857² = 3.447

-1.857² = 3.447

4.143² = 17.165

3.143² = 9.877

-0.857²= 0.735

Step 4: Find the sum of squares

8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857

Step 5: Apply the formula

$SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}\\\\SD = \sqrt{\dfrac{42.857}{7}} \\\\SD= 2.474$

Hence, the standard deviation of the data set is 2.474.

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