Selecting the Appropriate Measure of Central Tendency to Describe a Set of Data.

Measures of CentralTendency

Selecting the AppropriateMeasure of Central Tendency to

Describe a Set of Data

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

What are Measures of Central Tendency?

Consider the following math student:

– Lolita Bryant 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 Lolita is? (A student, B student, etc.)

It appears that Lolita is an A student

Grades: 96 94 90 100 86 9188 100 0 96 96 Find the mean, median, and mode of the grades Mean: about 85 Median: 94 Mode: 96 What caused Lolita’s mean (average) to be

an 85 instead of the A that we expected?

Think about it!

Pros and Cons

Pros Cons

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

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

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.

Strategies to Choose the Appropriate Measure of Central Tendency

Chloe’s Novel ReadingMonth Sept. Oct. Nov. Dec. Jan. Feb. March AprilNumber of 370 393 380 376 396 372 385

391Pages Read

If Chloe read only 125 pages during the month of May, whichmeasure of data changed the most? Why? A. mean B. median C. mode D. All measures were affected equally.

The following table shows the number of pages in novels that Chloe read for pleasure each month during the school year.

A retail store had total sales of $436, $650, $530, $500, $650, $489, and $423 last week. Which measure of data would make the store’s sales last week appear most profitable?

A. Mode B. Median C. Mean D. Range

Your Turn

If you are the team leader of a group of 7 workers who each make $12,000 a year. The president of your company makes $1,000,000 a year and the vice-president makes $600,000 a year. A report to the Department of Labor from the president

says the average salary of the employees is $169,600.

Which measure of central tendency is the president using in the report? Why? Which measure could you use to prove him wrong? Why

Think about it!

Your current allowance is $15 a week. You are trying to get your parents to raise your allowance so you find out the allowances of some of your friends - $25, 18, $18, $40, $0, $10, $0, and $22.

Which measure of central tendency will help convince your parents to raise your allowance?

A. Mean B. Median C. Mode D. Range

You have the following test scores: 89, 84, 79, 80, 81, and 55. What measure of central tendency would you give your parents to make your grades look better?

A. Mean B. Median C. Mode D. Range

Which measure of central tendency would you use to describe data on your classmates’ favorite type of cereal?

A. Mean B. Median C. Mode D. Range

Mr. Kern has a video store. The table shows his sales, to the nearest $10.

Figure it out!

Month SalesMay $330.00

June $450.00

July $420.00

August $380.00

In September, Mr. Kern takes a 2 week vacation and closes the store. His sales for that month were only $190. Which measure of central tendency changed the most with the month of low sales? Why?

A. MeanB. MedianC. Mode

If the manager at a department store says, “Size 36 is our best-selling men’s pants size,” what measure of central tendency is being used? How do you know?

A. Mean B. Median C. Mode D. Range

One more problem!