Question

The number of songs enjoyed from the band Aerosmith by a sample of teachers is below. 6,8,8,10,7,9. What is the mean of this sample? (There’s a like over the x) X= ? What is the standard deviation of this sample? S=?

Answer 1

The mean of the sample is 8 songs and the standard deviation is about 1.41 songs.

Step-by-step explanation:

To calculate the mean of a sample, you add up all the values in the sample and then divide the sum by the number of values. In this case, the sample contains 6, 8, 8, 10, 7, and 9 songs enjoyed by teachers. Adding these values together gives us a sum of 48. There are 6 values in the sample, so dividing the sum by 6 gives us a mean of 8 songs.

To calculate the standard deviation of a sample, you need to determine the variance first. Variance is calculated by finding the difference between each value in the sample and the mean, squaring that difference, adding up those squared differences, and finally dividing by the number of values minus one. For this sample, the mean is 8. The differences between each value and the mean are: -2, 0, 0, 2, -1, and 1. Squaring these differences gives: 4, 0, 0, 4, 1, and 1. Adding up the squared differences gives a sum of 10. Dividing by 6 - 1 = 5 gives a variance of 2. The standard deviation is the square root of the variance, so for this sample, the standard deviation is about 1.41 songs.