3.1 Measures of Center

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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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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.
St. Andrews

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

Red Lion

Salesianum

Sanford

Wilmington Friends

Caravel

Tuitions of Area High Schools

GROUP 2

GROUP 1

Tuition Activity
• Estimate the tuition of your school.

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

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

Find the Median
• 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.
Three Measures of Central Tendency
• Mean (sample mean): average of a data set
• Median: middle number of a data set
• Mode (modal): most frequent data point
Mean (or sample mean)
• Symbol is
• Formula to find the mean
• n = total number of items
• Σ= Greek letter SIGMA and means SUM
Mean (or sample mean)
• The mean is SENSITIVE to Extreme Values, called OUTLIERS.
• Why?

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

Median
• 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.
Median
• 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

Mode
• 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)
Finding values on Calculator
• 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