Power point chapter 2 sections 6 through 9

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1) The document discusses descriptive statistics such as percentiles, quartiles, measures of center, and measures of spread. It provides examples and explanations of how to calculate and interpret these statistical concepts. 2) Percentiles such as the 25th and 75th percentiles are used to describe the quartiles of a data distribution. The median and mean are common measures of center. Standard deviation and variance are frequently used to quantify the spread of values around the mean. 3) Worked examples demonstrate how to find percentiles, quartiles, measures of center and spread, and determine outliers using calculations and technology. Interpreting these statistical results in the context of a problem

Chapter 2

D E S C R I P T I V E S TA T I S T I C S
SECTIONS 6-9

2.6 Percentiles

 Quartiles are specific examples of percentiles. The first
quartile is the same as the 25th percentile and the third
quartile is the same as the 75th percentile.

 The nth percentile represents the value that is greater than or
equal to n% of the data.

 Jennifer just received the results
EXAMPLE of her SAT exams. Her SAT
Composite of 1710 is at the 73rd
Consider each of
the following
percentile. What does this mean?
statements about
percentiles.
 Suppose you received the highest
score on an exam. Your friend
scored the second-highest
score, yet you both were in the
99th percentile. How can this be?

Number
Frequency RF CRF
EXAMPLE of Tickets
0 6 0.08 0.08
The following data 1 18 0.24 0.32
set shows the
number of parking 2 12 0.16 0.48
tickets received.
3 11 0.15 0.63
4 9 0.12 0.75
5 6 0.08 0.83
6 5 0.07 0.90
7 4 0.05 0.95
8 2 0.03 0.98
9 1 0.01 0.99
10 1 0.01 1

 Find and interpret the 90th
EXAMPLE percentile.

The following data
set shows the  Find and interpret the 20th
number of parking
tickets received.
percentile.

 Find the first quartile, the
median, and the third quartile.

 Construct a box plot.

EXAMPLE  Find the inner quartile range of
the data set.
The following data
set shows the
number of parking
tickets received.  Do any of the data values appear
to be outliers

EXAMPLE

Find the mean 1. 4.5, 10, 1, 1, 9, 14, 4, 8.5, 6, 1, 9
median and mode of
the following data
set.

Use technology to
find statistical
information.

2.9 Measures of Spread

 The final statistics we would like to be able to find are
measures that tell us how spread out the data is about the
mean.

 The two statistics that are most commonly used to measure
spread are standard deviation and variation.

 Standard deviation gives us another way to identify possible
outliers: a data value might be an outlier if it is more than
two standard deviations from the mean.

2.9 Calculating Standard Deviation and Variance

EXAMPLE

Find the standard 1. 4.5, 10, 1, 1, 9, 17, 4, 8.5, 5, 1, 9
deviation and
variance of the data
set assuming that it
is a sample.

Use standard
deviation to
determine if any
values are possible
outliers.
Use technology to
find statistical
values.

In 2000 the mean age of a sample of females
Example in the U.S. population was 37.8 years with a
standard deviation of 21.8 years and the mean
age of a sample of males was 35.3 with a
standard deviation of 18.4 years.

In relation to the rest of their sex, which is
older, a 48 year old woman or a 45 year old
man?

Characterizing a distribution

1. Center, mean/median/mode
2. Skew
3. Spread

Characterizing a Data Distribution

Example: For each distribution described below, discuss the
number of peaks, symmetry, and amount of variation you
would expect to find.

- The salaries of actors/actresses.

- The number of vacations taken each year.

- The weights of calculators stored in the math library – half
are graphing calculators and half are scientific calculators.

HOMEWORK

2.13 #s 4a, b, c, 7, 10, 12, 13a, b, d, e, f, also construct a line
graph for the data from Publisher A and Publisher B, 16a part
i and iii, 16b, 21, 29, 30, 31

The document discusses various statistical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of variability (range, variance, standard deviation, percentiles, quartiles). It provides examples of calculating each measure for sample data sets. It also discusses how data can be organized and displayed graphically using histograms, bar graphs, and other visualizations. The goal of descriptive statistics is to summarize key aspects of a data set, such as its central tendency and variability, which provides critical information for understanding the data.

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TSTD 6251�� Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton

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TSTD 6251�� Fall 2014 SPSS Exercise and Assignment 1 20 Points In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise. Practice Example: Admission receipts (in million of dollars) for a recent season are given below for the n = 30 major league baseball teams: 19.4�� 26.6�� 22.9�� 44.5�� 24.4�� 19.0�� 27.5�� 19.9�� 22.8�� 19.0�� 16.9�� 15.2�� 25.7�� 19.0�� 15.5�� 17.1�� 15.6�� 10.6�� 16.2�� 15.6�� 15.4�� 18.2�� 15.5�� 14.2�� 9.5�� 9.9 10.7�� 11.9�� 26.7�� 17.5 Require: a.�� Compute the mean, variance and standard deviation. b.�� Find the sample median, first quartile, and third quartile. c.�� Construct a boxplot and interpret the distribution of the data. d.�� Discuss the distribution of this set of data by examining kurtosis and skewness �� statistics, such as if the distribution is skewed to one side of the distribution, and if the �� distribution shows a peaked/skinny curve or a spread out/flat curve. SPSS Procedures for Computing Summary Statistics : Enter the 30 data values in the first column of SPSS Data View Tab Variable View and name this variable receipts Adjust Decimals to 3 decimal points Type Admission Receipts ($ mn) in the Label column for output viewer Return to Data View and click A nalyze on the menu bar Click the second menu D e scriptive Statistics Click F requencies … Move Admission Receipts to the Variable(s) list by clicking the arrow button Click S tatistics … button at the top of the dialog box Now, you can select the descriptive statistics according to what the question requires.�� For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes except for P ercentile(s): and Va l ues are group midpoints . Click Continue to return to the Frequencies dialog box Click OK to generate descriptive statistic output which is pasted below: The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red. Statistics Admission Receipts N Valid 30 Missing 0 Mean 18.76333 Std. Error of Mean 1.278590 Median 17.30000 Mode 19.000 Std. Deviation 7.003127 Variance 49.043782 Skewness 1.734 Std. Error of Skewness .427 Kurtosis 5.160 Std. Error of Kurtosis .833 Range 35.000 Minimum 9.500 Maximum 44.500 Sum 562.900 Percentiles 10 10.61000 20 14.40000 25 15.35000 30 15.50000 40 15.84000 50 17.30000 60 19.00000 70 19.75000 75 22.82500 80 24.10000 90 26.69000 Admission Receipts Frequency Percent Valid Percent Cumulative Percent Valid 9.500 1 3.3 3.3 3.3 9.900 1 3.3 3.3 6.7 10.600 1 3.3 3.3 10.0 10.700 1 3.3 3.3 13.3 11.900 1 3.3 3.3 16.7 14.200 1 3.3 3.3 20.0 15.2.

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Math Exam HelpLive Exam Helper

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Power point chapter 2 sections 6 through 9

1. Chapter 2 D E S C R I P T I V E S TA T I S T I C S SECTIONS 6-9

2. 2.6 Percentiles  Quartiles are specific examples of percentiles. The first quartile is the same as the 25th percentile and the third quartile is the same as the 75th percentile.  The nth percentile represents the value that is greater than or equal to n% of the data.

3.  Jennifer just received the results EXAMPLE of her SAT exams. Her SAT Composite of 1710 is at the 73rd Consider each of the following percentile. What does this mean? statements about percentiles.  Suppose you received the highest score on an exam. Your friend scored the second-highest score, yet you both were in the 99th percentile. How can this be?

4. Number Frequency RF CRF EXAMPLE of Tickets 0 6 0.08 0.08 The following data 1 18 0.24 0.32 set shows the number of parking 2 12 0.16 0.48 tickets received. 3 11 0.15 0.63 4 9 0.12 0.75 5 6 0.08 0.83 6 5 0.07 0.90 7 4 0.05 0.95 8 2 0.03 0.98 9 1 0.01 0.99 10 1 0.01 1

5.  Find and interpret the 90th EXAMPLE percentile. The following data set shows the  Find and interpret the 20th number of parking tickets received. percentile.  Find the first quartile, the median, and the third quartile.  Construct a box plot.

6. 2.6 IQR and outliers 

7. Number Frequency RF CRF EXAMPLE of Tickets 0 6 0.08 0.08 The following data 1 18 0.24 0.32 set shows the number of parking 2 12 0.16 0.48 tickets received. 3 11 0.15 0.63 4 9 0.12 0.75 5 6 0.08 0.83 6 5 0.07 0.90 7 4 0.05 0.95 8 2 0.03 0.98 9 1 0.01 0.99 10 1 0.01 1

8. EXAMPLE  Find the inner quartile range of the data set. The following data set shows the number of parking tickets received.  Do any of the data values appear to be outliers

9. 2.7 Measures of Center 

10. EXAMPLE Find the mean 1. 4.5, 10, 1, 1, 9, 14, 4, 8.5, 6, 1, 9 median and mode of the following data set. Use technology to find statistical information.

11. Number Frequency RF CRF EXAMPLE of Tickets 0 6 0.08 0.08 The following data 1 18 0.24 0.32 set shows the number of parking 2 12 0.16 0.48 tickets received. 3 11 0.15 0.63 Find the mean, 4 9 0.12 0.75 median, and mode. 5 6 0.08 0.83 Use technology to 6 5 0.07 0.90 find statistical information. 7 4 0.05 0.95 8 2 0.03 0.98 9 1 0.01 0.99 10 1 0.01 1

12. 2.9 Measures of Spread  The final statistics we would like to be able to find are measures that tell us how spread out the data is about the mean.  The two statistics that are most commonly used to measure spread are standard deviation and variation.  Standard deviation gives us another way to identify possible outliers: a data value might be an outlier if it is more than two standard deviations from the mean.

13. 2.9 Calculating Standard Deviation and Variance

14. EXAMPLE Find the standard 1. 4.5, 10, 1, 1, 9, 17, 4, 8.5, 5, 1, 9 deviation and variance of the data set assuming that it is a sample. Use standard deviation to determine if any values are possible outliers. Use technology to find statistical values.

15. Number Frequency RF CRF EXAMPLE of Tickets 0 6 0.08 0.08 The following data 1 18 0.24 0.32 set shows the number of parking 2 12 0.16 0.48 tickets received. 3 11 0.15 0.63 Find the standard deviation and 4 9 0.12 0.75 variance of the data 5 6 0.08 0.83 set assuming that it is a sample. 6 5 0.07 0.90 Use standard 7 4 0.05 0.95 deviation to determine if any 8 2 0.03 0.98 values are possible 9 1 0.01 0.99 outliers. 10 1 0.01 1

16. In 2000 the mean age of a sample of females Example in the U.S. population was 37.8 years with a standard deviation of 21.8 years and the mean age of a sample of males was 35.3 with a standard deviation of 18.4 years. In relation to the rest of their sex, which is older, a 48 year old woman or a 45 year old man?

17. Characterizing a distribution 1. Center, mean/median/mode 2. Skew 3. Spread

18. Characterizing a Data Distribution

19. Characterizing a Data Distribution

20. Characterizing a Data Distribution

21. Characterizing a Data Distribution

22. Characterizing a Data Distribution

23. Characterizing a Data Distribution

24. Characterizing a Data Distribution

25. Characterizing a Data Distribution

26. Characterizing a Data Distribution

27. Characterizing a Data Distribution Example: For each distribution described below, discuss the number of peaks, symmetry, and amount of variation you would expect to find. - The salaries of actors/actresses. - The number of vacations taken each year. - The weights of calculators stored in the math library – half are graphing calculators and half are scientific calculators.

28. HOMEWORK 2.13 #s 4a, b, c, 7, 10, 12, 13a, b, d, e, f, also construct a line graph for the data from Publisher A and Publisher B, 16a part i and iii, 16b, 21, 29, 30, 31

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Power point chapter 2 sections 6 through 9

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