Question

Use SPSS Do not exceed more than 2 pages of output.

You were again promoted by the mayor for getting her good information about lead levels in dogs. She has appointed you the new senior health officer of the city of Sarasota. Your first task is to check the results of a report that the previous health officer completed. The mayor thinks there might be some calculation errors in the data presented. You need to determine the mean, median, mode, range, standard deviation and variance of the following data. Produce a graph that allows the mayor to determine if the data are normally distributed.

Legionnaires Cases/Month
5
1
5
7
10
9
7
11
7
10
9
15
9
3
13
13
9
16

Answer 1

Given the data as

The Sorted data set is

Mean:

We have, Sum

No. of terms

Median:

The median is the middle number in a sorted list of numbers.

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Mode: The mode of a set of data is the value in the set that occurs most often. therefore for this above data

Since 9 appears 4 times, We see that the mode is 9 .

Range:

The range is the difference between the highest and lowest values in the data set. so

Standard Deviation:

To find standard deviation we use the following formula

Here mean , so  We create the table

5	-3.8333	14.69418889
1	-7.8333	61.36058889
5	-3.8333	14.69418889
7	-1.8333	3.36098889
10	1.1667	1.36118889
9	0.1667	0.02778889
7	-1.8333	3.36098889
11	2.1667	4.69458889
7	-1.8333	3.36098889
10	1.1667	1.36118889
9	0.1667	0.02778889
15	6.1667	38.02818889
9	0.1667	0.02778889
3	-5.8333	34.02738889
13	4.1667	17.36138889
13	4.1667	17.36138889
9	0.1667	0.02778889
16	7.1667	51.36158889

Find the sum of numbers in the last column to get.

  

The standard deviation of the data set is:

Variance:

To find variance we use the following formula

Hence the variance of data set is