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Elementary Statistics Chapter 2

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Sidney Smith 01/24/2015 CH 2 HW Statistics 2-1 1. Five reasons for organizing data into a frequency distribution: a. To organize the data in a meaningful, intelligible way. b. To enable the reader to determine the nature or shape of the distribution. c. To facilitate computational procedures for measures of average and spread. d. To enable the researcher to draw charts and graphs for the presentation of data. e. To enable the reader to make comparisons among different sets. 2. Categorical Frequency Distributions is used for data that can be placed in specific categories. Grouped Frequency Distributions is used when the range of the data is large and the data must be grouped in to classes that are more than one unit in width. Ungrouped Frequency Distribution is used when the range of data has been organized into a frequency distribution and analyzed by looking for peaks and extreme values. (Cumulative Frequency Distribution is a distribution that shows the number of data values less than or equal to a specific value (usually an upper boundary).) 3. A frequency distribution should have five to twenty classes. Class width should be an odd number so that the midpoints of the classes are in the same place values as the data. 4. An Open Ended Frequency Distribution has either a first class with no lower limit or a last class with no upper limit. They are necessary to accommodate all the data. Class Boundaries Midpoint Width 5. 42.5-47.5 45 5 6. 124.5-131.5 128 7 7. 8.235-11.365 9.8 4.12 8. 16.25-18.55 17.4 3.2 9. Class width is not uniform. 10. Class limits overlap and class width is not uniform. 11. A class has been omitted. 12. Class width is not uniform. 13. CLASS TALLEY FREQ % F IIIII IIIII IIIII IIII 19 38% C IIIII IIIII IIII 14 28% B IIIII IIIII 10 20% A IIIII II 7 14% 50 100%

15.

CLASS 0 1 2 3 4 5 6

TALLEY II IIIII IIIII IIIII IIIII IIIII IIII IIIII III IIIII I IIII

FREQ 2 5 24 8 6 4 0

% 4% 10% 48% 16% 12% 8% 0%

Sidney Smith 01/24/2015 CH 2 HW Statistics 7 I 1 50 2% 100%

19.

CLASS 10-19 20-29 30-39 40-49 50-59 60-69 70-79

TALLEY II IIIII IIIII IIIII I IIIII IIIII IIIII II IIIII IIIII IIIII I

FREQ 0 2 16 17 10 5 1 51

% 0% 4% 31% 33% 20% 10% 2% 100%

2-2 1. 102 students do not have to enroll in the summer program.

Histogram
150 Frequency 100 50 0 1 2 3 Bin 4 5 More Frequency

Frequency Polygon
150 Frequency 100 50 0 1 2 Bin 3 4 5 Series2

Sidney Smith 01/24/2015 CH 2 HW Statistics

Ogive
150 Frequency 100 50 0 1 2 Bin 3 4 5 Series2 Series1

3. The majority of the states have 25 to 75 counties within them (I’m thankful it cumulated to 50…phew).

Sidney Smith 01/24/2015 CH 2 HW Statistics

4. 5.

Sidney Smith 01/24/2015 CH 2 HW Statistics

4. The distribution of faculty has a positive (increasing) distribution. 12 schools have more than 180 faculty.

Sidney Smith 01/24/2015 CH 2 HW Statistics

Sidney Smith 01/24/2015 CH 2 HW Statistics

7.
CLASS 21-29 30-38 39-47 48-56 57-65 66-74 75-83 LOWER MIDPOINT BOUND 25 34 43 52 61 70 79 UPPER BOUND 20.5 29.5 38.8 47.5 56.5 65.5 74.5 29.5 38.5 47.5 56.5 65.5 74.5 83.5 CUM FREQ FREQ 5 10 13 10 4 3 1

5 15 28 38 42 45 46

FREQ
14 12 10 8 6 4 2 0 21-29 30-38 39-47 48-56 57-65 66-74 75-83 FREQ

Sidney Smith 01/24/2015 CH 2 HW Statistics

FREQ

FREQ

21-29

30-38

39-47

48-56

57-65

66-74

75-83

CUM FREQ
50 45 40 35 30 25 20 15 10 5 0 0 20 40 60 80 100

CUM FREQ

2-3 1.

Sidney Smith 01/24/2015 CH 2 HW Statistics

4.
CONTINENT NORTH AMERICA EUROPE ASIA SOUTH AMERICA AUSTRALIA AFRICA FREQ 643 413 315 45 22 17

Sidney Smith 01/24/2015 CH 2 HW Statistics

PARETO
700 600 500 400 300 200 100 0

FREQ

Sidney Smith 01/24/2015 CH 2 HW Statistics 6.

12.…...

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