Data Description

Chapter 3 Data Description

3-1 Measures of Central Tendency ( page 3-3)

Measures found using data values from the entire population are called: parameter

Measures found using data values from samples are called: statistic

A parameter is a characteristic or measure obtained using data values from a specific population.

A statistic is a characteristic or measure obtained using data values from a specific sample.

The Measures of Central Tendency are:

• The Mean • The Median • The Mode • The Midrange

• The Mean

The mean is the sum of the values, divided by the total number of values.

Sample mean: [pic] where n is the sample size

Population mean: [pic] where N is the population size

• The Median

The median of a data set is the value in the center of the data when the set is arranged in order.

• The Mode

The mode is the value that occurs most often in a data set. If a data set has two values that occur with the same frequency that dataset is said to be bimodal.

• The Midrange

MR = [pic]

Example 1

Determine the 4 measures of central tendency of the data set in the following sample.

33 35 31 32 37 30 37 37 36 39

a) Mean [pic]

b) Median

30 31 32 33 35 36 37 37 37 39 ↑ MD = [pic]35.5

c) Mode: 37 (occurs 3 times)

d) Midrange: MR = [pic]
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Example 2

Determine the 4 measures of central tendency of the data set in the following sample.

56 58 57 59 53 58 51

• The Weighted Mean

The Weighted Mean of a variable X is found multiplying each value by the corresponding