Mathematics High School

consider the following data sets: variable a: 5 3 5 5 4 8 variable b: 3 1 1 4 2 1 calculate the sample covariance. a) 0.65 b) 2.30 c) -1.77 d) -0.20

Answers

Answer 1

The sample covariance between variable a and variable b is -0.2.

To calculate the sample covariance between two variables,

We want to do following steps:

1) Calculate the mean (average) of each variable.

2) Subtract the mean from each value in their respective variables.

3) Multiply the resulting differences for each pair of values.

4) Sum up all the products obtained in step 3.

5) Divide the sum by the number of data points minus 1 (sample size minus 1).

Let's calculate the sample covariance for the given data sets (variable a and variable b),

Variable a: 5, 3, 5, 5, 4, 8

Variable b: 3, 1, 1, 4, 2, 1

Step 1: Calculate the means of each variable.

Mean of variable a:

[tex](5 + 3 + 5 + 5 + 4 + 8) / 6 = 30 / 6 = 5[/tex]

Mean of variable b:

[tex](3 + 1 + 1 + 4 + 2 + 1) / 6 = 12 / 6 = 2[/tex]

Step 2: Subtract the mean from each value in their respective variables.

For variable a:

[tex](5 - 5), (3 - 5), (5 - 5), (5 - 5), (4 - 5), (8 - 5),0, -2, 0, 0, -1, 3[/tex]

For variable b:

[tex](3 - 2), (1 - 2), (1 - 2), (4 - 2), (2 - 2), (1 - 2),1, -1, -1, 2, 0, -1[/tex]

Step 3: Multiply the resulting differences for each pair of values.

[tex]0 * 1, -2 * -1, 0 * -1, 0 * 2, -1 * 0, 3 *-10, 2, 0, 0, 0, -3[/tex]

Step 4: Sum up all the products obtained in step 3.

[tex]0 + 2 + 0 + 0 + 0 + (-3) = -1[/tex]

Step 5: Divide the sum by the number of data points minus 1.

[tex]-1 / (6 - 1) = -1 / 5 = -0.2[/tex]

Therefore, the sample covariance between variable a and variable b is -0.2.

The correct option is d) -0.20.

Learn more about sample covariance here,

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