1. Frequency Distribution Dr. Wajed Hatamleh
WEEK 2
Frequency Distribution
Dr. Wajed Hatamleh
Dr. Wajed Hatamleh week 2

2. Learning Objectives
Recognize the difference between grouped and ungrouped data
Construct a frequency distribution
Construct a histogram
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3. Overview Descriptive Statistics Inferential Statistics
summarize or describe the important characteristics of a known set of population data
Inferential Statistics
use sample data to make inferences (or generalizations) about a population
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4. Important Characteristics of Data
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
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5. Ungrouped Versus Grouped Data
Ungrouped data
have not been summarized in any way
are also called raw data
Grouped data
have been organized into a frequency distribution
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6. WHAT THE HECK ARE ALL THOSE NUMBERS??? Example of Ungrouped Data
? ? ? ? ? ? ?
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7. Frequency Distributions
HELP!!
That’s what a frequency distribution is for—to help impose order on the data
A frequency distribution is a systematic arrangement of data values, with a count of how many times each value occurred in a dataset
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8. Key Concept
When working with large data sets, it is often helpful to organize and summarize data by constructing a table called a frequency distribution.
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9. Definition Frequency Distribution (or Frequency Table)
lists data values (either individually or by groups of intervals), along with their corresponding frequencies or counts
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10. Ungrouped Versus Grouped Data
Ungrouped data
have not been summarized in any way
are also called raw data
Grouped data
have been organized into a frequency distribution
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11. Example of Ungrouped Data42 30 53 50 52 55 49 61 74 26 58 40 28 36 33 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54
Ages of a Sample of
Nurses Managers from
KFH, KSA
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12. Frequency Distribution of Nursing Manager’s Ages at KFH
Class Interval Frequency 20-under under under under under under 80 1
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13. Data Range Smallest Largest 42 30 53 50 52 55 49 61 74 26 58 40 28 3633 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54
Smallest
Largest
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14. Number of Classes and Class Width
The number of classes should be between 5 and 15.
Fewer than 5 classes cause excessive summarization.
More than 15 classes leave too much detail.
Class Width
Divide the range by the number of classes for an approximate class width
Round up to a convenient number
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15. Class Midpoint
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16. Relative Frequency
Relative Class Interval Frequency Frequency 20-under under under under under under Total
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17. Cumulative Frequency Cumulative Class Interval Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total 50
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18. Class Midpoints, Relative Frequencies, and Cumulative Frequencies
Relative Cumulative
Class Interval Frequency Midpoint Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total
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19. Cumulative Relative Frequencies
Relative Cumulative Relative
Class Interval Frequency Frequency Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total
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20. Frequency Distributions
Another example
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23. Lower Class Limits
are the smallest numbers that can actually belong to different classes
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24. Lower Class Limits Lower Class Limits
are the smallest numbers that can actually belong to different classes
Lower Class
Limits
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25. Upper Class Limits Upper Class Limits
are the largest numbers that can actually belong to different classes
Upper Class
Limits
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26. Class Boundaries
are the numbers used to separate classes, but without the gaps created by class limits
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27. number separating classes
Class Boundaries
number separating classes
- 0.5
99.5
199.5
299.5
399.5
499.5
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28. number separating classes
Class Boundaries
number separating classes
Class
Boundaries
- 0.5
99.5
199.5
299.5
399.5
499.5
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29. midpoints of the classes
Class Midpoints
midpoints of the classes
Class midpoints can be found by adding the lower class limit to the upper class limit and dividing the sum by two.
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30. midpoints of the classes
Class Midpoints
midpoints of the classes
Class
Midpoints
49.5
149.5
249.5
349.5
449.5
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31. Class Width Class Width
is the difference between two consecutive lower class limits or two consecutive lower class boundaries
Class
Width
100
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32. Reasons for Constructing Frequency Distributions
1. Large data sets can be summarized. 2. Can gain some insight into the nature of data. 3. Have a basis for constructing graphs.
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33. Constructing A Frequency Table
1. Decide on the number of classes (should be between 5 and 20) . 2. Calculate (round up).
(highest value) – (lowest value)
class width 
number of classes
3. Starting point: Begin by choosing a lower limit of the first class.
4. Using the lower limit of the first class and class width, proceed to list the lower class limits.
5. List the lower class limits in a vertical column and proceed to enter the upper class limits.
6. Go through the data set putting a tally in the appropriate class for each data value.
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34. Relative Frequency Distribution
class frequency
sum of all frequencies
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35. Relative Frequency Distribution
11/40 = 28%
12/40 = 40%
etc.
Total Frequency = 40
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36. Cumulative Frequency Distribution Cumulative Frequencies
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37. Frequency Tables
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38. Recap In this Section we have discussed
Important characteristics of data
Frequency distributions
Procedures for constructing frequency distributions
Relative frequency distributions
Cumulative frequency distributions
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39. A table that lists data values along with their counts is
An olgive.
A frequency distribution.
A cumulative table.
A histogram.
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40. The smallest numbers that can actually belong to different classes are
Upper class limits.
Class boundaries.
Midpoints.
Lower class limits.
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41. The smallest numbers that can actually belong to different classes are
Upper class limits.
Class boundaries.
Midpoints.
Lower class limits.
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