Question

Please answer using your own words (i.e., don't quote directly from the text).: Describe the three different measures of central tendency and how their values are determined. For each, give two examples (other than those given in the text) of their appropriate use.

Answer 1

Describe the three different measures of central tendency and how their values are determined.

Central tendency is the single measure in which one value can be used to describe a complete set of data. This is usually the central value or the middle of the data distribution.

Three different measures:

1. Mean
2. Median
3. Mode

Mean: The sum of each data value in the total set divided by the number of data values in the total set.
Median: The middle value in the data distribution when the data set is arranged in ascending or descending order
Mode: The most repeated data value in the data distribution.

For each, give two examples (other than those given in the text) of their appropriate use.

Example 1:
Time spent in hours playing by a teenager on 7 days of the week.

Data set: 2,2,3,4,6,2,4

Mean: 2+2+3+3+4+4+3=21

Median: 2,2,3,3,4,4,3. 3 is the median value

Mode: The most commonly occurring value is 3.

Example 2:

Data set: 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60 (Ages)

Mean: The mean of people getting retired from workforce at a private firm can be calculated.

54+54+54+55+56+57+57+58+58+60+60 = 623

623 / 11 = 56.6 years.

This is the mean age.

Median: 52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

Arranged in ascending order, the median is between 56 & 57.

Mode: 52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

The most commonly occurring value is 54. Therefore mode is 54.

They are useful in indicating the most typical or central value in a data set that helps identify patterns for further analysis.