Question

The following data was collected from 10 visitors to Disneyland. A researcher stood at the entrance gate and interviewed the first 10 families that agreed to participate. Each family was asked, “How many times have you been to Disneyland?” The data values were: 1, 1, 2, 2, 2, 2, 3, 3, 4, 7. The average number of visits was calculated and reported.

Calculate the standard deviation of the data values.

Answer 1

The standard deviation for the sample of 10 families is 1.68 (Rounding to two decimal places)

Explanation:

1. The first step to calculate the standard deviation is to find out the mean, this way:

Mean = (1 + 1 + 2 + 2 + 2 + 2 + 3 + 3 + 4 + 7)/10

Mean = 27/10 = 2.7

2. Now we calculate the variance, this way:

Variance = [(1 - 2.7)²+(1 - 2.7)²+(2 - 2.7)²+(2- 2.7)²+(2 - 2.7)²+(2 - 2.7)²+(3- 2.7)²+(3 - 2.7)²+(4 - 2.7)²+(7- 2.7)²]/10

Variance = [2.89 + 2.89 + 0.49 + 0.49 + 0.49 + 0.49 + 0.09 + 0.09 + 1.69 + 18.49]/10

Variance = 28.1/10 = 2.81

3. Finally we calculate the standard deviation, this way:

Variance = Standard deviation²

√Variance = Standard deviation

√2.81 = Standard deviation

Standard deviation = 1.68 (Rounding to two decimal places)