Post on 04-Jan-2016
transcript
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