Frequency Distribution Objectives: Create Frequency Distributions Analyze Frequency Distribution.
Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number...
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Transcript of Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number...
![Page 1: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/1.jpg)
Chapter 3Frequency Distributions
![Page 2: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/2.jpg)
Frequency Distributions
• A frequency distribution lists the number of times, or frequency (f), each raw score (X) in a set of score (distribution) appears.
X f
3 2
2 3
1 2
Ex: 1, 1, 2, 2, 2, 3, 3
It’s easy to spot the mode.
![Page 3: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/3.jpg)
Constructing a Frequency Distribution
14, 14, 10, 8, 14, 16, 8, 10, 10, 8, 10, 16, 16, 6, 20, 16, 9, 10, 17, 10, 18, 14, 14, 8
Step 1: Find the highest and lowest scores.
Step 2: Construct a table including all numbers. By convention, the highest score is listed first and the lowest score is listed last.
![Page 4: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/4.jpg)
Constructing a Frequency Distribution
Step 3: Make a tally mark for each score.
Step 4: Count up the tally marks and fill in the frequency column.
![Page 5: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/5.jpg)
Frequency Distributions
Like inferential statistics, descriptive statistics, and graphs, frequency distributions are judgment aids. They make it easier for a scientist or another person to react meaningfully to the results of an experiment or to other information (data).
![Page 6: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/6.jpg)
Grouped frequency distribution
In a grouped frequency distribution, the total range of scores is divided into a number of mutually exclusive (nonoverlapping) and collectively exhaustive categories (class intervals) and the frequency of scores in each category is reported.– Categories typically are of the same width (e.g., 1-4, 5-9, 10-
14).– The number of categories depends on the data of interest; the
textbook recommends 10-15 categories.– To determine the size of class intervals, subtract the lowest
score from the highest score and divide by the number of desired class intervals.
![Page 7: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/7.jpg)
Six Groups
![Page 8: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/8.jpg)
Eleven Groups
![Page 9: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/9.jpg)
Sixteen Groups
![Page 10: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/10.jpg)
Your Turn: Activity #1
17, 3, 16, 16, 28, 5, 3, 23, 31, 19, 2, 20, 19, 17, 27, 25, 18, 15, 19, 6, 22, 9, 15, 22, 1, 18, 16
1. Make 10 categories for your frequency distribution.
2. Create a frequency distribution using the above data.
3. Put your name on your paper.
![Page 11: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/11.jpg)
Discrete vs. Continuous Variables
• Discrete variables can take only specific values (usually whole numbers).– Ex: The number of people in a family can be
three, but it can’t be 3.45.
• Continuous variables can take an infinite number of values. – Ex: The amount of alcohol consumed can
take on any value. For example, someone could consume 29.5698359167 oz. of tequila.
![Page 12: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/12.jpg)
Apparent vs. Real LimitsX f
8
7
6
5
• Apparent Limits: When we are working with continuous variables, this table won’t do. It has gaps in it. (In fact, the probability of getting a value of exactly 6 is infinitely small.)
• Real Limits: We can transform this table into one that includes all possible values in the range.
• In this case, we will use the original value ± .5 to eliminate the gaps.
X f
7.5 – 8.5
6.5 – 7.5
5.5 – 6.5
4.5 – 5.5
![Page 13: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/13.jpg)
Percentage (or Relative) Distributions
It is possible to express frequencies as percentages, which may make frequency distributions more useful as judgment aids.
f = frequency (of a particular score)N = total number of scores
![Page 14: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/14.jpg)
Why is it Useful?
• One of the main advantages is that you can compare results from samples of different sizes.
![Page 15: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/15.jpg)
Activity #2• Write on a small piece of paper the number of times you think
most university students have had sexual intercourse in the last 30 days.
• Pass the paper to the end of your row.
• Our categories: 0, 1, 2-5, 6-10, 11+
• Change the number in each category to a percentage and construct a frequency table
• Put your name on the paper.
![Page 16: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/16.jpg)
How many times in the last 30 days have you had sexual intercourse?
0 1 2-5 6-10 11+0%
10%
20%
30%
40%
50%
60%
MaleFemaleTotal
How many times in the last 30 days have most students had sexual intercourse?
0 1 2-5 6-10 11+0%
10%
20%
30%
40%
50%
60%
MaleFemaleTotal
(from Wechsler & Kuo, 2000)
![Page 17: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/17.jpg)
Cumulative Frequency Distributions
• Starting with the lowest score and moving to the highest, the frequency is accumulated.
• For example: X
3
2
1
f
2
3
2
Cum f
7
5
2
![Page 18: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/18.jpg)
Why is it useful?
• The Cumulative Frequency Distribution allows you to see the median and the distribution of scores around the median.
![Page 19: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/19.jpg)
Cumulative Percentage Distributions
• Cumulative percentage frequencies also can easily be calculated.
• Use the data from the previous chart and this formula:
• You try.X
3
2
1
f
2
3
2
Cum f
7
5
2
Cum %age
100
71
29
![Page 20: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/20.jpg)
Why is it Useful?
• The Cumulative Percentage Distribution allows you to see the percentage of scores that fall at or below a given score.
![Page 21: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/21.jpg)
Students’ Estimates of Binge Drinkers in their School
RESPONSE (%) %age Cum %age
0-9 8.2 8.2
10-19 11.7 19.8
20-29 14.4 34.2
30-39 16 50.2
40-49 9.2 59.4
50-59 10.3 69.7
60-69 9.7 79.4
70-79 6.7 86.1
80-100 3.2 89.3
Don’t know 10.7 100.0
![Page 22: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/22.jpg)
Combine All Methods
X
3
2
1
f
2
3
2
Cum f
7
5
2
Cum %age
100
71
29
%age
29
43
29
![Page 23: Chapter 3 Frequency Distributions. Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in.](https://reader035.fdocuments.in/reader035/viewer/2022062301/56649c895503460f9494220a/html5/thumbnails/23.jpg)
Homework
• Prepare for Quiz 3 over Chapter 3
• Read Chapter 4
• Finish Chapter 3 Homework (check course website or WebCT)
• Prepare for Basic Math Re-test