Algebra 1 9-1 Measures of center and spread - Mrs. Johnston

ALGEBRA 1 9-1 MEASURES OF CENTER AND SPREAD

USE MEAN, MEDIAN, RANGE AND INTERQUARTILE RANGE TO CHARACTERIZE THE CENTER AND SPREAD OF DATA

QUARTILES

When the data is place in numerical order

1) The median (2nd quartile) is the number in the middle of the list *calculator will find this MedianX

2) The first quartile is the number in the middle of the lower half *calculator will find this Q1X

3) The third quartile is the number in the middle of the upper half *calculator will find this Q3X

4) The interquartile range (IQR) is the difference between the first and third quartile

lower half

upper half

Example: 1, 2, 3, 4, 5, 5, 6, 7, 8, 10, 12

first quartile median third quartile

11/8/2017

MEASURES OF CENTER

Mean ? The numeric average - Found by adding all the data and dividing by the number of data entries - The calculator finds it and labels it x

Median ? The middle value of the data when it is placed in numerical order

- If there are two numbers in the middle, average them

Mode ? The number that appears in your list most often - There can be a tie, or there can be no mode

MEASURES OF SPREAD

Range ? the difference between the highest and lowest numbers in the list

*Calculator finds the MaxX and the MinX, you need to do the subtracting

Interquartile range ? the difference between the third and first quartile

*Calculator finds Q3X and Q1X, you need to do the subtracting

Standard Deviation ? a way to identify how spread out the data is

*Calculator finds it x

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EXAMPLE

Enter the list below into a spreadsheet on your calculator 36, 18, 12, 10, 9

Use Menu, Statistics, Stat Calculations, and One-Variable Statistics to get your calculator to find the stats you need. Tab past Num of List 1 to OK, Tab down the next screen to OK to get your data to appear in your speadsheet.

Identify the Mean = Median = First Quartile = Third Quartile = Range = IQR = Standard Deviation =

EXAMPLE OF COMPARING DATA

Enter the data for the MLB Players Average Ages off of page 359 in your book.

Find the statistics below:

Mean =

Range =

Median =

IQR =

First Quartile = Third Quartile =

Standard Deviation =

EXAMPLE OF COMPARING DATA

Enter the data for the NFL Players Average Ages off of page 359 in your book.

Find the statistics below:

Mean =

Range =

Median =

IQR =

First Quartile =

Standard Deviation =

Third Quartile =

11/8/2017

COMPARE YOUR DATA

Compare the statistics for the NFL Players and MLB Players... What do you notice about the typical ages of players? What do you notice about the variation of ages? What do you notice about the mean and median? What do you notice about the IQR and range?

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CHANGING DATA

Find the statistics for the following data

77, 86, 84, 93, 90

Mean = Median = First Quartile = Third Quartile =

Range = IQR = Standard Deviation =

Change the 90 to 92 and recalculate your stats

Mean =

Range =

Median =

IQR =

First Quartile =

Standard Deviation =

Third Quartile =

PRACTICE ? STORE A

Enter the data below:

Ages of Customers: 18, 20, 19, 16, 21, 20

Find the statistics below:

Mean =

Range =

Median = First Quartile = Third Quartile =

IQR = Standard Deviation =

CHANGING DATA

Which values, if any, changed because the 90 was replaced with a 92?

11/8/2017

Which values, if any, remained the same even though the 90 was changed to a 92?

PRACTICE ? STORE B

Enter the data: Ages of Customers: 52, 48, 60, 53, 50, 57

Find the statistics below:

Mean =

Range =

Median =

IQR =

First Quartile =

Standard Deviation =

Third Quartile =

Compare the statistics for Store A and Store B and tell why this might be.

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