MEASURES OF CENTRAL TENDENCY

James Reese and Cheuk Wong

MEAN

MEDIANMODE

Mean (Average)

The mean, or average is the sum of the data divided by the amount of data in it.

It is used to show what is normal. Pro: It’s a way to show what is

normal. Con: It is greatly affected by

outliers. Another Con: It sometimes results in

a nonterminating, nonrepeating decimal.

Median

The median is the piece of data in the middle of the data set if there is an odd amount of data, or the number between the middle two numbers if there is an even amount.

It is used to show what is in the middle and is often more accurate than the mean, as it isn’t affected by outliers nearly as much.

Pro: It shows what is in the middle. Con: It sometimes isn’t part of the data set.

Mode

The mode is the part of the data with the most entries, such as if in a data table, if 5 came in 3 times, 2 came in once, and 4 came in 5 times, 4 would be the mode.

It would be used to show the most popular choice in a poll.

Pro: It shows what is the most popular.

Con: It doesn’t show anything else.

Necessary Data Needed

Each measure of central tendency needs a single set of data.

1 SET

Example From Outside Source

In this stem and leaf plot, the mean is about 65.385, the median is 60, and the mode is 75.

This shows how many people watched TV for how many minutes a day. From the measures of central tendency, it can be concluded that most students watch about 60 to 75 minutes of TV per day.

Image from kasiesmaps.blogspot.com

Our Constructed Example

We took a poll of how many minutes people in Mrs. Ellwood’s fourth period class thought they studied for any given test.

The results were as follows: 0, 0, 0, 0, 7, 7, 10, 10, 15, 20, 30, 40, 90, and 120. Therefore, the median was 10, the mode was 0, and the average was about 24.93.

Our Problem

If Mrs. Ellwood’s time spent studying of 2 hours were added to the data (the old mean was 24.93 minutes and there were 14 inputs), what would the new average be? (Round to the nearest tenth)

ANSWER TO THE PROBLEMAbout 31.3

How to Answer the Problem The results form the original were(0, 0, 0,

0, 7, 7, 10, 10, 15, 20, 30, 40, 90, and 120) Find the average: 24.93 minutes 14 inputs Mrs. Ellwood’s time: 2 hours (120 minutes)1) 24.93*14+120 =469.022) 469.02/(14+1) =31.2683) Round 31.268 to 31.3