Thinking Mathematically

Statistics:12.2 Measures of Central Tendency

The MEAN

The mean of a set of quantitative data is the sum of the measurements divided by the number of measurements contained in the data set. (the average)

mean x

n

Exercise Set 12.2 #5

Compute the mean of the following scores:

100, 40, 70, 40, 60

Calculating the Mean from a Frequency Distribution

mean xf

nWherex represents each data value.f represents frequency of that data value.xf represents the sum of all the products obtained by multiplying each data value by its frequency.n represents the total frequency of the distribution.

Example Mean from a Frequency Distribution

Exercise Set 12.2 #9

Compute the mean for the data items in the frequency distribution: Score x Frequency f

1 1

2 3

3 4

4 4

5 6

6 5

7 3

8 2

The MEDIAN

• To find the median of a group of data items,1. Arrange the data items in order, from smallest to largest.2. If the number of data items is odd, the median is the item in the middle of the list.3. If the number of data items is even, the median is the mean of the two middle data items.

Exercise Set 12.2 #15Find the median of 91, 95, 99, 97, 93, 95

• How do you calculate the median of a group of data items described by a frequency distribution?

The MODE

• The mode is the data value that occurs most often in a data set.

• If no data items are repeated, then the data set has no mode. If more than one data value has the highest frequency, then each of these data values is a mode.

Exercise Set 12.2 #27Find the mode of 91, 95, 99, 97, 93, 95

• How do you determine the mode of a group of data items described by a frequency distribution?

The Midrange

• The midrange is found by adding the lowest and highest data values and dividing the sum by 2.

Midrange = lowest data value+highest data value

2Exercise Set 12.2 #37

Find the midrange for 7, 4, 3, 2, 8, 5, 1, 3

• How do you calculate the midrange of a group of data items described by a frequency distribution?

Thinking Mathematically

Statistics:12.2 Measures of Central Tendency