Question

Calculate the mean and var of the following data. You must give a reason for each formula you use and then show the steps of

your calculations.
Student classes attended
A 10
B 8
C 10
D 7
E 15

Answer 1

The mean of the data is 10, and the variance is 7.6.

Explanation:

To calculate the mean and variance of the given data, we'll follow these steps:

Step 1: Calculate the mean.

Step 2: Calculate the deviations from the mean.

Step 3: Square the deviations.

Step 4: Calculate the sum of squared deviations.

Step 5: Divide the sum of squared deviations by the number of data points to find the variance.

Let's perform the calculations:

Step 1: Calculate the mean.

Mean = (10 + 8 + 10 + 7 + 15) / 5 = 50 / 5 = 10

The mean of the data is 10.

Step 2: Calculate the deviations from the mean.

Deviation for A = 10 - 10 = 0

Deviation for B = 8 - 10 = -2

Deviation for C = 10 - 10 = 0

Deviation for D = 7 - 10 = -3

Deviation for E = 15 - 10 = 5

Step 3: Square the deviations.

Squared deviation for A = 0^2 = 0

Squared deviation for B = (-2)^2 = 4

Squared deviation for C = 0^2 = 0

Squared deviation for D = (-3)^2 = 9

Squared deviation for E = 5^2 = 25

Step 4: Calculate the sum of squared deviations.

Sum of squared deviations = 0 + 4 + 0 + 9 + 25 = 38

Step 5: Divide the sum of squared deviations by the number of data points to find the variance.

Variance = Sum of squared deviations / Number of data points = 38 / 5 = 7.6