These are the solutions to the descriptive statistics exercises. You are strongly advised to work out your own solutions before you look at these. I don't actually expect you to calculate the standard deviation by hand. However, you might consider using spreadsheet software to create the necessary table and use the sums at the bottom of the columns to calculate the mean and standard deviation.

The data below lists the number of times the students in a class were absent.

0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 4, 4, 5, 1, 0, 2, 0, 0, 2, 2, 0

First, sort the data in ascending order.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 5

Find the sum of the data values and calculate the mean. Use the mean to find the deviations and the squares of the deviations. Find the sum of the squares of the deviations and calculate the standard deviation. In the table below, I have also found the sum of the deviations just to help convince you that the sum of the deviations is always zero.

Use these values to calculate the mean and the standard deviation:

The data below lists the grades of the students in a class. Each grade is associated with a corresponding number of grade points as follows:

Grade | Points |

A | 4 |

B | 3 |

C | 2 |

D | 1 |

F | 0 |

F, A, C, B, B, A, B, B, A, A, A, C, A, B, C, D, B, A, A, C, D, C, A, C

Sort the grade point data in ascending order. (It is not necessary to include the letter grades as I have done here.)

F, D, D, C, C, C, C, C, C, B, B, B, B, B, B, A, A, A, A, A, A, A, A, A 0, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4

Find the sum of the data values and calculate the mean. Use the mean to find the deviations and the squares of the deviations. Find the sum of the squares of the deviations and calculate the standard deviation. In the table below, I have also found the sum of the deviations just to help convince you that the sum of the deviations is always zero.

Use these values to calculate the mean and the standard deviation:

A titration experiment in a chemistry class resulted in the data below.

0.109, 0.111, 0.110, 0.110, 0.105, 0.110, 0.111, 0.110, 0.110, 0.111, 0.109, 0.111, 0.109, 0.112, 0.109, 0.109, 0.111, 0.110, 0.112, 0.112, 0.109, 0.110, 0.110, 0.109, 0.113, 0.108, 0.105, 0.110, 0.109, 0.109, 0.110, 0.110, 0.110, 0.104, 0.109, 0.110, 0.111

Sort the data in ascending order.

0.104, 0.105, 0.105, 0.108, 0.109, 0.109, 0.109, 0.109, 0.109, 0.109, 0.109, 0.109, 0.109, 0.109, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.110, 0.111, 0.111, 0.111, 0.111, 0.111, 0.111, 0.112, 0.112, 0.112, 0.113

Find the sum of the data values and calculate the mean. Use the mean to find the deviations and the squares of the deviations. Find the sum of the squares of the deviations and calculate the standard deviation. In the table below, I have also found the sum of the deviations just to help convince you that the sum of the deviations is always zero.

Use these values to calculate the mean and the standard deviation:

A simple random sample of camshafts at an automotive engine plant is collected and the lengths of the camshafts measured. The resulting lengths (in millimeters) are given below.

600.8, 599.4, 599.4, 599.8, 599.4, 598.4, 599.0, 599.0, 598.6, 599.8, 599.6, 599.2, 600.6, 599.2, 600.4, 600.4, 601.2, 599.4, 600.0, 599.8, 599.8, 599.6, 600.2

Sort the data in ascending order.

598.4, 598.6, 599.0, 599.0, 599.2, 599.2, 599.4, 599.4, 599.4, 599.4, 599.6, 599.6, 599.8, 599.8, 599.8, 599.8, 600.0, 600.2, 600.4, 600.4, 600.6, 608.0, 601.2

Use these values to calculate the mean and the standard deviation: