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Welcome to MM150
Seminar 9:
Statistics, Part II
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Measures of Central Tendency
Measures of Central Tendency section 9.1
The mean of a set of numbers is the average.
Example: 12, 5, 7, 16
mean = (12+5+7+16)/4 = 10
Measures of Central Tendency section 9.1
Example: The mean of five test scores is 81.
What is the sum of the test scores?
Measures of Central Tendency section 9.1
page 368 #37
Measures of Central Tendency section 9.1
The median of a set of numbers is the middle number.
Example: 5, 3, 11, 9, 8, 15, 2
Order the numbers: 2,3,5,8,9,11,15
The median is the middle number = 8
Measures of Central Tendency section 9.1
If there are an even number of values:
Example: 5, 3, 11, 9, 8, 15, 2, 20
Order the numbers: 2,3,5,8,9,11,15, 20
The median is the average of the
middle numbers = (8+9)/2 = 8.5
Measures of Central Tendency section 9.1
Mode = most frequently occurring value (may have more
than one mode)
ex: 1,1,2,2,2,5,7,8,8,8,9
Midrange = (low val + high val) / 2
Measures of Central Tendency section 9.1
Values: 2 3 7 9 10 13 17 21 22 25 30
Median = "50th percentile" = Q2
First Quartile = median of lower half = Q1
Third Quartile = median of upper half = Q3
Measures of Central Tendency section 9.1
Values:
15 19 19 20 22 23 24
24 24 25 26 27 29 30
32 34 34 35 36 39 42
What are Q1 , Q2 and Q3 ?
Measures of Central Tendency section 9.1
Page 368 #51
Measures of Dispersion
Measures of Dispersion section 9.2
Two data sets with mean = 50
Data Set 1: 48, 49, 50, 51, 52
Data Set 2: 10, 20, 50, 80, 90
What is the difference?
Measures of Dispersion section 9.2
Range = high val - low val
Example: 11, 9, 6, 12, 17
What is the range?
Measures of Dispersion section 9.2
Standard Deviation: "average" deviation from the mean
Data Set: 2, 3, 5, 8, 9, 11, 18
The Normal Curve
The Normal Curve section 9.3
Data which approximates a Normal Distribution
The Normal Curve section 9.3
The Normal Curve section 9.3
Use table 9.4 to find the area to the right of z = 1.34
The Normal Curve section 9.3
Use table 9.4 to find the area to the left of z = 1.62
The Normal Curve section 9.3
Use table 9.4 to find the area between z = -1.32 and
z = -1.64
The Normal Curve section 9.3
Page 394 #49
The Normal Curve section 9.3
Page 394 #50
The Normal Curve section 9.3
Assume that math SAT scores are normally distributed with
a mean of 500 and a standard deviation of 100.
What percent of students who took the test have a math
score below 550?
The Normal Curve section 9.3
Assume that math SAT scores are normally distributed with
a mean of 500 and a standard deviation of 100.
What percent of students who took the test have a math
score above 650?
The Normal Curve section 9.3
Assume that math SAT scores are normally distributed with
a mean of 500 and a standard deviation of 100.
What percent of students who took the test have a math
score between 550 and 650?
Linear Regression
