Download 3.3 Messures of Spread

Statistics Notes: Measures of Spread ­ Grouped Data
3.3 Grouped Data and Measures of Central Tendency.
The data in the table represents the 3­year rate of return of a randomly selected sample of small­capitalization growth mutual funds.
What is the mode of the data?
We don't have enough information.
What are the max and min for the data?
We don't have enough information, but the minimum lies between 10 and 15 and the maximum between 45 and 50.
Create a frequency polygon for the data.
Create a histogram of the data.
What is the shape of the distribution? Skew right.
12
12
6
4
2
0
10
Frequency
Histogram
8
8
Frequency Polygon
6
4
2
0 5 10 15 20 25 30 35 40 45 50
3­year rate of return
0
0 5 10 15 20 25 30 35 40 45 50
3­year rate of return
12
10
Frequency
Frequency
10
8
6
Connection between a Histogram and a Frequency Polygon
4
2
0
0 5 10 15 20 25 30 35 40 45 50
3­year rate of return
1
Statistics Notes: Measures of Spread ­ Grouped Data
What is the mean of the data? What is the standard deviation of the data?
mean
We're finding the Sample Standard Deviation s = 9.24
Formulas for Grouped Data
Population Mean:
Sample Mean:
Population Variance:
Population Standard Deviation:
Sample Variance:
Sample Standard Deviation:
1
2
Statistics Notes: Measures of Spread ­ Grouped Data
Weighted Mean: Marissa just completed her 1st semester in college. She earned the following grades:
"A" in her 4­hour statistics course,
"B" in her 3­hour sociology class,
"A" in her 3­hour psychology class,
"C" in her 5­hour computer programming course
"A" in her 1­hour drama class
Find Marissa's GPA. Weighted Mean formula:
where wi is the weight of the ith observation
and xi is the value of the ith observation
HW: Statistics Homework Section 3.3
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