3.1 measures of center

3.1 Measures of CenterObjectives:By the end of this section, I will beable to…

1) Calculate the mean for a given data set.

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

3) Find the mode of a data set.

4) Describe how skewness affects these measures of center.

Tuitions of Area High Schools

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 Padua Red Lion Salesianum Sanford Wilmington Friends Caravel

GROUP 1 GROUP 2

Tuition Activity1) 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.

Find the Median5) Each student on the end says “One”6) The next two students say “Two”7) The next two students say “Three”8) Keep going until you find the middle

person, or the median tuition.9) Report your median tuition to the

class.10) Find the mean of your tuitions.

Three Measures of Central Tendency

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

2) Median: middle number of a data set

3) Mode (modal): most frequent data point

Mean (or sample mean)

Symbol is

Formula to find the mean

n = total number of itemsΣ = Greek letter SIGMA and means

SUM

xx

n

x

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

MedianAlways put data items in

ORDER FIRST!Then find the middle term of

the data setIf there is no exact middle,

find the average of the TWO MIDDLE TERMS.

MedianThe median is NOT sensitive

to OUTLIERS.

Why?90, 92, 91, 87, 90, 95, 96, 93, 88, 87, 4646, 87, 87, 88, 90, 90, 91, 92, 93, 95, 96

ModeOrder data firstFind the data point that occurs

the mostYou do not have to have a modeYou 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 Calculator1) Input data into STAT → EDIT → LIST2) Then Quit (2nd MODE) and go to HOME SCREENFind the MEAN3) 2nd STAT → MATH → 3.MEAN4) 2nd 1 to get L1. Hit ENTER.Find the MEDIAN5) 2nd STAT → MATH → 4.MEDIAN6) 2nd 1 to get L1. Hit ENTER