Question

What is the standard deviation of the data?

As an introduction to probablity, a student is asked to roll
a fair, six-sided number cube seven times. The results of
those seven rolls are shown below.
a) 1.41
b) 1.53 1, 4, 4, 4, 4, 6,5
c) 2.33
d) 5

Answer 1

To find the standard deviation of the data set (1, 4, 4, 4, 4, 6, 5), you must calculate the mean, subtract the mean from each data point to find the differences, square these differences, sum them up, find the variance, and then take the square root of the variance. The standard deviation is approximately 1.53.

Step-by-step explanation:

The standard deviation of the data can be found by following these steps:

1. Calculate the mean (average) of the numbers given by adding them all up and then dividing by the number of data points.
2. Subtract this mean from each of the numbers to get their differences from the mean.
3. Square each of these differences.
4. Add up all of the squared differences.
5. Divide this total by the number of data points minus one to get the variance.
6. Take the square root of the variance to find the standard deviation.

Applying these steps to the data set of die rolls provided (1, 4, 4, 4, 4, 6, 5):

1. The mean is (1+4+4+4+4+6+5)/7 = 28/7 = 4.
2. The differences from the mean are -3, 0, 0, 0, 0, 2, 1.
3. The squared differences are 9, 0, 0, 0, 0, 4, 1.
4. The sum of the squared differences is 9+0+0+0+0+4+1 = 14.
5. The variance is 14/(7-1) = 14/6 = 2.33.
6. The standard deviation is the square root of 2.33, which is approximately 1.53.

Thus, the standard deviation of the data is approximately 1.53, which corresponds to option b).