Measures of Center

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Measures of Center
Measures of Center
Mean
Median
Mode
Range
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Measures of Center
Use of TI-83 to determine measures of center.
One variable statistics 1-Var Stats
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The Sample Standard Deviation
Calculate the mean, median, and mode for each
team.
Calculate the range for each team.
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The Sample Standard Deviation
Sample Standard Deviation
1. For each piece of data determine the
difference with the mean.
2. Determine the sum of the squares of the
deviations.
3. Take an average of the squared deviations.
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The Sample Standard Deviation
Sample Variance
Sample Standard Deviation
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The Sample Standard Deviation
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The Sample Standard Deviation
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The Sample Standard Deviation
The data represents 10 IQ scores.
a. Use the defining formula to obtain the
standard deviation of the 10 IQs.
b. Use the computing formula to obtain the
standard deviation of the 10 IQs.
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The Sample Standard Deviation
The table gives the number of tornados that
touched down in the U.S. during each month in
2002.
a. Determine the range of the data.
b. Calculate the sample standard deviation of the
data from the defining formula.
c. Calculate the sample standard deviation of the
data from the computing formula.
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Five Number Summary
Quartiles
Arrange data in increasing order and determine
median.
1st quartile is median of data set that lies
below the median of the entire set.
2nd. Quartile is the median of the entire set.
3st quartile is median of data set that lies
above the median of the entire set.
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Five Number Summary
Weekly TV-viewing time.
Find the quartiles of the data.
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Five Number Summary
5 number summary
5 number summary of a data set Min, Q1, Q2, Q3,
Max.
Interquartile Range IQR
IQR Q3 Q1
Lower and upper limits Used to find outliers.
Lower Limit Q1 1.5xIQR
Upper Limit Q3 1.5xIQR
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Five Number Summary
The data table is a sample of 21 patients at a
hospital and the length of stay for each.
a. Determine the Quartiles
b. Determine the IQR.
c. Construct a Boxplot
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Use of Samples
Population Mean
Population Standard Deviation
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Use of Samples
Parameter A descriptive measure for a population.
Statistic A descriptive measure for a sample.
z-score The number of standard deviations from
the mean.
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Use of Samples
a. Compute the sample mean height
b. Compute the sample standard deviation, s
c. Assuming a population, compute the population
mean height.
d. Compute the population standard deviation.
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Use of Samples