Measures of Central Tendency and Range

Choosing Measures of Central Tendency or Range to Describe a Set of Data and Justifying the Choice for a Particular Situation (TEKS 7.12A and B)

What do Measures of Central Tendency show us?

Numbers or pieces of data that can represent the whole set of data

What are Measures of Central Tendency?

Mean The arithmetic average of the set of data. The most common measure of central tendency.

Median The median is the middle score in a set of data. Half the data will be above the median, and half below

when data is ordered.

Mode The mode is the most frequently occurring value or

most popular choice

Consider the following math student: John Doe has gotten the following grades on

homework: 96 94 90 100 86 91

88 100 0 96 96

Without calculating – what type of student do you think John Doe is? (A student, B student, etc.)

It appears that John is an A student

Grades:96 94 90 100 86 91

88 100 0 96 96

Find the mean, median, and mode of the grades

Mean: about 85Median: 94Mode: 96

What caused John’s mean (average) to be an 85 instead of the A that we expected?

Pros and Cons Pros Mean

Most familiar measure Uses all the data

Median Not affected by extreme

values Easy to compute Always exists

Mode Easiest to find Not affected by extreme

values Good for categorical data Doesn’t always exist

Cons Mean

Affected by extreme values (very high or very low)

Median Doesn’t use all data values Data must be properly

ordered

Mode Doesn’t use all data values Not always descriptive of

entire data set Not necessarily unique

Strategies to Choose the Appropriate Measure of Central Tendency

Order the data first to make it easier to find the median and mode.

Look for outliers (numbers that are a lot higher or lower than the rest of the set – an extreme value) – they affect the mean the most!

Is the data numerical or categorical (words)? Start with the easiest – mode, then median, then

mean. You may find you don’t need to work out all of them.

Using Measures of Central Tendency and Range to find Missing Data Identify which measure of central tendency you

are given or if the range is given. Mode – Check to see if the mode of the data in

the table and the mode given are the same. Median – Put the median given in the middle

and order the data around it. Range – Are you missing the highest or the

lowest piece of data? Mean – work backwards.

Answer the following using the strategies you have developed.

Super Bowl Champion Team Defeated Team

XLIII (2009) Pittsburg, 27 Arizona, 23

XLII (2008) New York, 17 New England, 14

XLI (2007) Indianapolis, 29 Chicago, 17

XL (2006) Pittsburg, 21 Seattle, ___

XXXIX (2005) New England, 24 Philadelphia, 21

XXXVIII (2004) New England, 32 Carolina, 29

XXXVII (2003) Tampa Bay, ___ Oakland, 21

XXXVI (2002) New England, 20 St. Louis, 17

The table below is a list of past Super Bowl games, the champion teams, and the defeated teams.

Tampa Bay was the highest scoring team in the years listed. The range of the scores of the champion teams is 31. What was Tampa Bay’s score?

Seattle was the lowest scoring team in the years listed. The range of the scores of the defeated teams is 19. What was Seattle’s score?

Patrice records the number of calories sheburns while exercising each day, as shownbelow.

Day 1: 250 caloriesDay 2: 350 caloriesDay 3: 400 caloriesDay 4: 250 caloriesDay 5: 300 calories

How many calories must Patrice burn on thesixth day to have a mean of 300 caloriesburned for the 6 days?

F 0 caloriesG 150 caloriesH 250 caloriesJ 310 calories

Randy and his 5 friends played a card game in which the person with the lowest final score wins. The table below shows the final scores for all the players except Erica.

If Erica won the game and the range of the scores was 17, what was Erica’s score?

F 104G 106H 140J 124

Player Score

Randy 121

Erica

Jon 119

Sam 107

Dawn 123

Maya 112