Problem 32E

A sample of the personnel files of eight employees at the Pawnee location of Acme Carpet Cleaners, Inc., revealed that during the last six-month period they lost the following number of days due to illness:

2 |
0 |
6 |
3 |
10 |
4 |
1 |
2 |

A sample of eight employees during the same period at the Chickpee location of Acme Carpets revealed they lost the following number of days due to illness.

2 |
0 |
1 |
0 |
5 |
0 |
1 |
0 |

As the director of human relations, compare the two locations. What would you recommend?

Solution :

Step 1 of 1:

Our goal is :

We need to find compare the two locations.

Given 8 employees at the Pawnee location of Acme Carpet Cleaners.

So n=8.

Consider the data is

2, 0, 6, 3, 10, 4, 1, 2.

Now we have to calculate range.

First we have to arrange in ascending order.

0, 1, 2, 2, 3, 4, 6, 10.

Here the maximum value = 10 and the minimum value = 0.

The range formula is

Range = Maximum value-Minimum value

Range = 10-0

Range = 10

Therefore, the range is 10.

First we have to arrange in ascending order.

0, 1, 2, 2, 3, 4, 6, 10.

Then we take the 2 middle 2 and 3 values.

Now we have to add the 2 values and divide by 2.

Median =

Median =

Median = 2.5

Therefore, the median is 2.5.

Now we have to find the mean.

The mean formula is

Mean () =

Mean =

Mean =

Mean = 3.5

Therefore, the mean is 3.5.

Given 8 employees during the same period at the Chickpea location.

So n=8.

Consider the data is

2, 0, 1, 0, 5, 0, 1, 0.

Now we have to calculate range.

First we have to arrange in ascending order.

0, 1, 2, 2, 3, 4, 6, 10.

Here the maximum value = 10 and the minimum value = 0.

The range formula is

Range = Maximum value-Minimum value

Range = 5-0

Range = 5

Therefore, the range is 5.

First we have to arrange in ascending order.

0, 0, 0, 0, 1, 1, 2, 5.

Then we take the 2 middle 0 and 1 values.

Now we have to add the 2 values and divide by 2.

Median =

Median =

Median = 0.5

Therefore, the median is 0.5.

Now we have to find the mean.

The mean formula is

Mean () =

Mean =

Mean =

Mean = 1.125

Therefore, the mean is 1.125.

The Pawnee and Chickpea table is given below.

Location |
Range |
Median |
Mean |

Pawnee |
10 |
2.5 |
3.5 |

Chickpea |
5 |
0.5 |
1.25 |

Therefore, the mean and median location were higher, but there was also a more variation in Pawnee.