Measures of Central Tendency

Algebra 2

An average is a number that is representative group of data. There are three types of averages:

Mean- the sum of the data divided by the number of pieces

Median-is the value in the middle of a set of ranked data

Mode – is the piece of data that occurs most frequently

Mean Example

Find the mean age of a group of volunteers at an American Red Cross office is the ages of the individuals are 27, 18, 48, 34, and 48.

The Mean is 35 years

The mean represents the balancing point of a set of data.

27+18+48+34+48 5

Median Example

Determine the median of the volunteers’ ages from the American Red Cross. 27, 18, 48, 34, and 48.

Ranking the data from smallest to larges gives 18, 27, 34, 48, 48

Since 34 is the value in the middle, it is the median

Median (cont..)

If there are an even number of pieces of data, the median will be mean of the two middle numbers.

Determine the median of the following sets of data:a) 7, 23, 14, 15, 9, 14, 9, 10

b) 7, 8, 8, 8, 9, 107, 9, 9, 10, 12, 14, 14, 15 Median is 11

The data is ranked. The median is 8

Mode

Determine the mode of volunteers’ ages of 27, 18, 48, 34 and 48.

The mode is 48 because it occurs twice and the other data occur only once.

Mode (cont..)

Consider the following data:

1, 2, 13, 12, 15, 8, 7

This data has no mode.

The salaries of eight selected teachers rounded to the nearest thousand dollars are 40, 25, 28, 35, 42, 60, 60, 73. For this set of data, determineA) meanB) medianC) mode

45

41

60

Mean vs. Median

The mean is used when each piece of data is to be considered.

The mean is the only average that can be affected by any change in the set of data; it is the most sensitive.

When there is an outlier, it could effect the mean by increasing or decreasing it. In this case, the median should be used.

Consider a set of exam scores:0, 16, 19, 65, 65, 65, 68, 69, 70, 72, 73, 73, 75,

78, 80, 85, 88, 92. Which average could best represent these grades?

Mean?Median?

Mean is 64.06

Median is 71

Since only 3 of the 18 scores fall below the mean, the mean would not be considered a good representative score. The median of 71 would be the betteraverage to use.