Notes 2.3

Measures of Central Tendency

Central Tendency

• A measure of central tendency is a value that represents a typical or central entry of a data set. The most common ones are mean, median and mode.

• Mean: the sum of all the entries, then divided by the number of entries in the data set

Find the mean

• 12, 18, 19, 2, 18, 31, 24, 30, 9, 11, 14, 16, 18

• Median: is the middle data entry when the data is sorted is ascending (from smallest to greatest) or descending (from greatest to smallest) order.

• Find the median• 8 9 11 1 14 2 15 17 18 19 31 24 9

• Mode: the entry with the greatest frequency. If no entry is repeated the data set has no mode. If two numbers have the same amount of frequency both numbers are the mode.

• Ex 1 11 14 11 14 15 17 18 19 20

• Ex 2 4 8 9 14 15 8 19 21 7 31

Warm Up

Find the mean, median and mode.Number of time someone has gone fishing.1 0 4 0 5 0 34 0 1 0 2 4 0 0 0 0 2 1 0

Notes 2.3 Part 2

Weighted Mean

Outlier

• An outlier is a data entry that is far removed from the other data entries.

• Do the following data sets have an outlier.• 1) 4 5 8 4 5 7 1 4 34 5 7 8 5

• 2) 1 2 3 4 4 3 2 5 1 3 5 4 3 4 2

• Which measure of central tendency best describes a typical data entry?

• It all depends on whether the data entries have a outlier. – If the data set has an outlier the median is best– If a data set does not have an outlier the mean is

best. – The mode is almost never the best to describe a

data set.

• The mean is heavily influenced by an outlier that is why it is not the best method to describe a data set.

4 2 3 5 42 56 = 11.25Mean is 11.2

• The median is not influenced by an outlier therefore when an outlier is present, it is the best method to describe

4 2 3 5 422 3 4 5 42X X X X Median is 4

Weighted mean

• Weighted mean: is the mean of a data set whose entries have varying weights. A weighted mean is given by

Weighted Mean

Source Score x Weight w xw Test 82 .50Midterm 92 .15Final 72 .20Lab 98 .10HW 100 .05

∑w = ∑xw =

Weighted Mean

Source Score x Weight w xw Test 82 .50 41Midterm 92 .15 13.8Final 72 .20 14.4Lab 98 .10 9.8HW 100 .05 5

∑w = ∑xw =

Weighted Mean

Source Score x Weight w xw Test 82 .50 41Midterm 92 .15 13.8Final 72 .20 14.4Lab 98 .10 9.8HW 100 .05 5

∑w = 1.00 ∑xw = 84

Warm Up

Frequency Major Salary10 Math 68000

Science 7200051 History 40000

Find the weighted mean

Warm Up

Frequency Major Salary24 Math 6800031 Science 7200051 History 40000

Find the weighted mean

Notes 2.3 (Part 3)

Grouped Data

Grouped Data Equation

Useful for when there are a lot of data entries.

2 4 9 10 10 10 11 11 12 13 14 15 17 17 17 17 17 18 18 18 18 19 19 20 21 21 21 24 25 27 28 28 28 29 31

Grouped Data Mean Equation

Grouped Data Example

Age F Midpoint (x) xf0-8 29-17 1518-26 1227-35 6 ∑∫= ∑x∫=

Grouped Data Example

Age F Midpoint (x) xf0-8 2 49-17 15 1318-26 12 2227-35 6 31

∑∫= ∑x∫=

Grouped Data Example

Age F Midpoint (x) xf0-8 2 4 89-17 15 13 19518-26 12 22 26427-35 6 31 186

∑∫= ∑x∫=

Grouped Data Example

Age F Midpoint (x) xf0-8 2 4 89-17 15 13 19518-26 12 22 26427-35 6 31 186

∑∫= 35 ∑x∫= 653

Example #1

∑x∫ = 625 = 18.66∑∫ 35

Notes 2.3 (Part 4)

Finding GPA

Shapes of Distribution

Go to page 63 and copy the four shapes of distribution. Make sure to copy the shape of the graph.

1.Symmetric2.Uniform3.Skewed Left4.Skewed Right

How to find your GPA

All classes are not created equal in colleges and universities. Some are worth 1 credit, 2 credit, 3 credits and some are even worth 6 to 7 credits.

Lets calculate a sample GPA

Example 1

B in one 3 unit classD in one 5 unit class

Example 1

B in one 3 unit classD in one 5 unit class

Class Unit/Credit Grade Total

Example 1

B in one 3 unit classD in one 5 unit class

Class Unit/Credit Grade Total1 3 3 91 5 1 5

Example 1

B in one 3 unit classD in one 5 unit class

Class Unit/Credit Grade Total1 3 3 91 5 1 5

∑unit= ∑total=

Example 1

B in one 3 unit classD in one 5 unit class

Class Unit/Credit Grade Total1 3 3 91 5 1 5

∑unit= 8 ∑total=14

Example 1

Class Unit/Credit Grade Total1 3 3 91 5 1 5

∑unit= 8 ∑total=14

∑total = 14 = 1.75 GPA ∑unit 8