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# 3.1 Measures of Center - PowerPoint PPT Presentation

3.1 Measures of Center. Objectives: By the end of this section, I will be able to… Calculate the mean for a given data set. Find the median, and describe why the median is sometimes preferable to the mean. Find the mode of a data set. Describe how skewness affects these measures of center.

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Objectives:

By the end of this section, I will be

able to…

• Calculate the mean for a given data set.

• Find the median, and describe why the median is sometimes preferable to the mean.

• Find the mode of a data set.

• Describe how skewness affects these measures of center.

St. Elizabeth’s

St. Joseph's Prep, Philly

St. Marks

St. Thomas More

Tatnall

Tower Hill

Ursuline

Wilmington Christian

Aquinas

Archmere

Cardinal O'Hara, Phillly

Father Judge, Philly

Malvern Prep, Philly

Monsignor Bonner, Philly

Padua

Red Lion

Salesianum

Sanford

Wilmington Friends

Caravel

Tuitions of Area High Schools

GROUP 2

GROUP 1

• Estimate the tuition of your school.

Hint: All tuitions fall between \$4,000 and \$50,000.

2) Write your estimate on your slip of paper.

3) Get into the two groups and get in order from the lowest tuition to the highest tuition.

• Each student on the end says “One”

• The next two students say “Two”

• The next two students say “Three”

• Keep going until you find the middle person, or the median tuition.

• Report your median tuition to the class.

• Find the mean of your tuitions.

• Mean (sample mean): average of a data set

• Median: middle number of a data set

• Mode (modal): most frequent data point

• Symbol is

• Formula to find the mean

• n = total number of items

• Σ= Greek letter SIGMA and means SUM

• The mean is SENSITIVE to Extreme Values, called OUTLIERS.

• Why?

90, 92, 91, 87, 90, 95, 96, 93, 88, 87, 46

• Always put data items in ORDER FIRST!

• Then find the middle term of the data set

• If there is no exact middle, find the average of the TWO MIDDLE TERMS.

• The median is NOT sensitive to OUTLIERS.

• Why?

90, 92, 91, 87, 90, 95, 96, 93, 88, 87, 46

46, 87, 87, 88, 90, 90, 91, 92, 93, 95, 96

• Order data first

• Find the data point that occurs the most

• You do not have to have a mode

• You can have more than one mode

• Write down what you think the average tuition is for area private high schools.

• Find the mean, median, and mode of the tuitions of area high schools.

Skewness and Measures of Center

• For RIGHT-skewed distributions, the mean > median.

• For LEFT-skewed distributions, the mean < median.

• For SYMMETRIC distributions, the mean = median (roughly)

• Input data into STAT → EDIT → LIST

• Then Quit (2nd MODE) and go to HOME SCREEN

Find the MEAN

• 2nd STAT → MATH → 3.MEAN

• 2nd 1 to get L1. Hit ENTER.

Find the MEDIAN

• 2nd STAT → MATH → 4.MEDIAN

• 2nd 1 to get L1. Hit ENTER