The mean is the average: take all the values, lump them into a pile, and divide them equally among the all the contributors.

#3 Calculate the mean of the weights : 14, 16, 14, 14, 15, 13, 15, 17, 13, 14. __________ oz.

Procedure to find the mean:

1) The sum of the weights is 14+16+14+ 14+15+13+15+17+13+14 = 145

2) Divide the sum by the number of weights (10): = 14.5

3) The mean weight is 14.5 oz.

The symbol for the mean (of a sample) is , pronounced "x bar". So = 14.5 oz.

Here are the sorted weights: 13, 13, 14, 14, 14, 14, 15, 15, 16, 17.

The median is the middle value in a sorted list. If there is no middle, then the median is the average of the two measurements that straddle the middle.

#4 Find the median of the weights : 13, 13, 14, 14, 14, 14, 15, 15, 16, 17. __________ oz.

Procedure to find the median:

1) Sort the weights 13, 13, 14, 14, 14, 14, 15, 15, 16, 17.

2) Find the middle item in the list or the average of the two middle items.

13, 13, 14, 14, 14, 14, 15, 15, 16, 17 (14 +14) / 2 = 14

3) The median weight is 14 oz.

The mode is the most frequently occurring measurement (mode = fashion). There may be no mode or there may be more than one mode. The modes of 1, 3, 2, 2, 1, 2, 6, 6, 6, 2, 4 are 2 and 6.

#5 What is the mode of the weights of bags of chips? __________________

Procedure to find the mode:

1) It is helpful to sort the scores: 13, 13, 14, 14, 14, 14, 15, 15, 16, 17

2) Find the most frequent weight-- in this case, 14.

3) The mode (or modal weight) is 14 oz.

#6 Find the mean, median, and mode for the 11 salaries of this advertising company. The data are sorted.

Salaries and wages of each person at one business

mean salary ____________ median salary _____________ modal salary ______________

#7 Which is a better guide to the income of the whole group, the mean, median, or the mode, and why?

Now back to the chips. Calculate the mean weight of the packages coming off a second production line.

Sample weights from Line 2: 15, 14, 12, 13, 13, 18, 14, 14, 15, 17 oz.

You should get 14.5 oz. The mean is the same a production line 1, but there is something else going on.

#8 Identify the difference between the two production lines which is not shown in the mean.

Which production line is working best, according to our statistics?

Extreme values located away from the main group of data are known as outliers.

For example, suppose our sample of net weights contained the following:

15, 14, 12, 13, 31, 18, 14, 14, 15, 17

#9. Does this set contain an outlier, and can it be explained?

Does the salary data contain an outlier?

The mean, median and mode are referred to as measures of location because they each give an idea about the center of a group of values. These measures along with measures of dispersion are known as measures of central tendency. For a set of data with outliers, the median describes the whole data set better than the mean. The mean will be pulled toward extreme values. The median is less affected by extreme values. Few calculators have median or the mode keys, but computer statistics programs will produce all three of these statistics. If there are no outliers, and we choose one number to describe the data, it is most often the mean.

#10. Practice: Find the mean, the median, and the mode of the family sizes of the your class or group.

Use the nuclear family you grew up with, excluding pets.

Your own family size: ______________

List the data from your whole class: ________________________________________________________

The statistics for your class:

mean family size ______________ median size ______________ modal size ______________