Download 3.5 Descriptive Measures: Populations

Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
GOALS:
1. Understand difference between a population and sample.
2. Compute means and standard deviations for both populations and samples.
Study Ch. 3.5, # 195, 207, 209
Class Notes: Prof. G. Battaly, Westchester Community College, NY
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Class Notes
3.5 Descriptive Measures, Population
SAMPLE POPULATION
STATISTICS PARAMETERS MEAN
STD DEV
VARIANCE
MEDIAN
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Class Notes
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©G. Battaly 2015
1
Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
Given the following heights of basketball players:
67, 72, 76, 76, 84
I Regard this data as a sample, compute: a) the sample mean
b) the sample standard deviation
II. Regarding this data as a population, compute:
c) the population mean
d) the population standard deviation
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Class Notes
Statistics Home Page
3.5 Descriptive Measures, Population
#152. Given the following heights of basketball players:
Regard this data as a sample, compute: 67, 72, 76, 76, 84
a) the sample mean
b) the sample standard deviation
67
72
76
76
84
375
Regarding this data as a population, compute:
c) the population mean
d) the population standard deviation
μ
σ
Χ
s
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
©G. Battaly 2015
Class Notes
2
Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
#152. Given the following heights of basketball players:
Regard this data as a sample, compute: 67, 72, 76, 76, 84
a) the sample mean
b) the sample standard deviation
67
72
76
76
84
375
Regarding this data as a population, compute:
c) the population mean
d) the population standard deviation
μ
σ
Χ
s
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes
3.5 Descriptive Measures, Population
Χ
#152. Given the following heights of basketball players:
Regard this data as a sample, compute: 67, 72, 76, 76, 84
a) the sample mean
b) the sample standard deviation
67
72
76
76
84
Regarding this data as a population, compute:
c) the population mean
d) the population standard deviation
Χ
s
μ
σ
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
©G. Battaly 2015
Class Notes
3
Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
#124. Given the following heights of basketball players:
67, 72, 76, 76, 84
Since n = N for this example, the sample mean = population mean
But, the sample stdev ≠ population stdev Why?
Conclude:
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes
3.5 Descriptive Measures, Population
Consider the data sets:
a) Regarding this data as a sample, compute s for each set (2 dec places).
b) Regarding this as a population, compute δ for each set (2 dec places).
c) For which data set is the sample std dev closest to the population std dev?
If both sample and population std dev are computed, will they be
closer together if the data set is large or if it is small? Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
©G. Battaly 2015
Class Notes
4
Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
#137. Consider the data sets:
c) For which data set is the sample std dev closest to the population std dev?
If both sample and population std dev are computed, will they be closer in value if the data set is large or small? Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes
3.5 Descriptive Measures, Population
#137. Consider the data sets:
c) For which data set is the sample std dev closest to the population std dev?
If both sample and population std dev are computed, will they be
closer together if the data set is large or if it is small? Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
©G. Battaly 2015
Class Notes
5
Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
Suppose: Tests are returned and your grade is a 71.
Class average is a 65, and the standard deviation is 18.0.
How many standard deviations is your grade from the mean?
What if your grade is 80 and the class standard deviation is 15.0? How many standard deviations is your score from the mean?
Class Notes
Statistics Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Ans: 0.33, 1.0
3.5 Descriptive Measures, Population
Suppose: Tests are returned and your grade is a 71.
Class average is a 65, and the standard deviation is 18.0.
How many standard deviations is your grade from the mean?
What if your grade is 80 and the class standard deviation is 15.0? How many standard deviations is your score from the mean?
Class Notes
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Ans: 0.33, 1.0
©G. Battaly 2015
6
Descriptive Measures, Populations
September 28, 2015
3.5 Descriptive Measures, Population
z ­ Score: Standardized Variable
Number of Standard Deviations from the Mean
For each x, can compute:
For standardized variable, Mean = 0
Standard deviation = 1
For most distributions, most of the data lies
within 3 standard deviations of the mean.
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes
Ans: 0.33, 1.0
©G. Battaly 2015
7