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Summarizing Data with Frequency Tables Pictures of Data Measures of Center Measures of Variation Measures of Position Exploratory Data Analysis (EDA). Chapter 2 and 3 Descriptive Statistics. Descriptive Statistics

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Chapter 2 and 3 descriptive statistics

Summarizing Data with Frequency Tables

Pictures of Data

Measures of Center

Measures of Variation

Measures of Position

Exploratory Data Analysis (EDA)

Chapter 2 and 3Descriptive Statistics


Chapter 2 and 3 descriptive statistics

Descriptive Statistics

summarize or describethe important characteristics of a known set of population data

Inferential Statistics

use sample data to make inferences (or generalizations) about a population

2 -1 Overview


Chapter 2 and 3 descriptive statistics

1. Center: A representative or average value that indicates where the middle of the data set is located

2. Variation: A measure of the amount that the values vary among themselves

3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed)

4. Outliers: Sample values that lie very far away from the vast majority of other sample values

5. Time: Changing characteristics of the data over time

Important Characteristics of Data


Chapter 2 and 3 descriptive statistics

Frequency Table

lists classes (or categories) of values, along with frequencies (or counts) of the number of values that fall into each class

2-2 Summarizing Data With Frequency Tables


Chapter 2 and 3 descriptive statistics

Qwertry Keyboard Word Ratings

2 2 5 1 2 6 3 3 4 2

4 0 5 7 7 5 6 6 8 10

7 2 2 10 5 8 2 5 4 2

6 2 6 1 7 2 7 2 3 8

1 5 2 5 2 14 2 2 6 3

1 7


Chapter 2 and 3 descriptive statistics

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Table 2-3

Frequency Table of Qwerty Word Ratings


Lower class limits

are the smallest numbers that can actually belong to different classes

Lower Class Limits


Lower class limits1

are the smallest numbers that can actually belong to different classes

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Lower Class Limits


Lower class limits2

are the smallest numbers that can actually belong to different classes

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Lower Class Limits

Lower Class

Limits


Upper class limits

are the largest numbers that can actually belong to different classes

Upper Class Limits


Upper class limits1

are the largest numbers that can actually belong to different classes

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Upper Class Limits

Upper Class

Limits


Chapter 2 and 3 descriptive statistics

are the numbers used to different classesseparate classes, but without the gaps created by class limits

find gap between classes

divide it by 2

add to upper class limit

subtract from lower class limit

Class Boundaries


Chapter 2 and 3 descriptive statistics

number different classesseparating classes

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Class Boundaries

- 0.5

2.5

5.5

8.5

11.5

14.5


Chapter 2 and 3 descriptive statistics

number different classesseparating classes

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Class Boundaries

- 0.5

2.5

5.5

8.5

11.5

14.5

Class

Boundaries


Chapter 2 and 3 descriptive statistics

midpoints different classesof the classes

add class limits then divide by 2

Class Midpoints


Chapter 2 and 3 descriptive statistics

midpoints different classesof the classes

Rating

Frequency

0 - 1 2 20

3 - 4 5 14

6 - 7 8 15

9 - 10 11 2

12 - 13 14 1

Class Midpoints

Class

Midpoints


Chapter 2 and 3 descriptive statistics

is the difference between two consecutive lower class limits or two consecutive class boundaries

difference between class boundaries

difference between class midpoints

Class Width


Chapter 2 and 3 descriptive statistics

is the difference between two consecutive lower class limits or two consecutive class boundaries

Rating

Frequency

3 0 - 2 20

3 3 - 5 14

3 6 - 8 15

3 9 - 11 2

3 12 - 14 1

Class Width

Class Width


Chapter 2 and 3 descriptive statistics

1. Be sure that the classes are mutually exclusive. limits or two consecutive class boundaries

2. Include all classes, even if the frequency is zero.

3. Try to use the same width for all classes.

4. Select convenient numbers for class limits.

5. Use between 5 and 20 classes.

6. The sum of the class frequencies must equal the number of original data values.

Guidelines For Frequency Tables


Example find the class midpoint class bounds and class width

temperature limits or two consecutive class boundaries

Frequency

96.5 - 96.8 1

96.9 - 97.2 8

97.3 - 97.6 14

97.7 - 98.0 22

98.1 - 98.4 19

98.5 - 98.8 32

98.9 - 99.2 6

99.3 - 99.6 4

Example: Find the class midpoint, class bounds and class width


Chapter 2 and 3 descriptive statistics

1. Decide on the number of classes . limits or two consecutive class boundaries

2. Determine the class width by dividing the range by the number of classes (range = highest score - lowest score) and round up.

Constructing A Frequency Table

range

class width  round up of

number of classes

3. Select for the first lower limit either the lowest score or a convenient value slightly less than the lowest score.

4. Add the class width to the starting point to get the second lower class limit, add the width to the second lower limit to get the third, and so on.

5. List the lower class limits in a vertical column and enter the upper class limits.

6. Represent each score by a tally mark in the appropriate class.

  • Total tally marks to find the total frequency for each class.


Chapter 2 and 3 descriptive statistics

Figure 2-1 limits or two consecutive class boundaries


Chapter 2 and 3 descriptive statistics

class frequency limits or two consecutive class boundaries

relative frequency =

sum of all frequencies

Relative Frequency Table


Chapter 2 and 3 descriptive statistics

Relative limits or two consecutive class boundaries

Frequency

Rating

Rating

Frequency

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

0 - 2 38.5%

3 - 5 26.9%

6 - 8 28.8%

9 - 11 3.8%

12 - 14 1.9%

Relative Frequency Table

20/52 = 38.5%

14/52 = 26.9%

etc.

Total frequency = 52

Table 2-5


Chapter 2 and 3 descriptive statistics

Cumulative limits or two consecutive class boundaries

Frequency

Rating

Frequency

Rating

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Less than 3 20

Less than 6 34

Less than 9 49

Less than 12 51

Less than 15 52

Cumulative Frequency Table

Cumulative

Frequencies

Table 2-6


Frequency tables
Frequency Tables limits or two consecutive class boundaries

Cumulative Frequency

Relative

Frequency

Rating

Rating

Frequency

Rating

Less than 3 20

Less than 6 34

Less than 9 49

Less than 12 51

Less than 15 52

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

0 - 2 38.5%

3 - 5 26.9%

6 - 8 28.8%

9 - 11 3.8%

12 - 14 1.9%

Table 2-3

Table 2-5

Table 2-6


Qwerty and dvorak keyboard ratings

Dvorak limits or two consecutive class boundaries

Relative

Frequency

Qwerty

Relative

Frequency

Rating

Rating

0 - 2 38.5%

3 - 5 26.9%

6 - 8 28.8%

9 - 11 3.8%

12 - 14 1.9%

0 - 2 63.5%

3 - 5 36.5%

6 - 8 0%

9 - 11 0%

12 - 14 0%

Qwerty and Dvorak Keyboard Ratings