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PSYC 2002
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Steven Carroll
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Lecture 2

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Psychology

PSYC 2002

Steven Carroll

Winter

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Lecture 2: frequency distributions
What is a frequency distribution?
- What does ‘frequency’mean?
• The ‘commonness’of occurrence
• ‘How often does thing X happen?’
Based on a 1996 study of US college students
- Average number of drinks per week by GPA
• 3.3 per week =Astudent
• 4.8 per week= B student
• 6.1 per week= C student
• 9 per week= D/F student
- This is an ordinal scale, because it is on an alphabetical order
What is a frequency distribution?
- An organised tabulation showing the number of individuals located in each category on a
scale of measurement
- Can be either a table (‘news’example) or a graph (drink example)
- Frequency distributions always show two things:
• The categories that make up the scale
• The frequency, or number of individuals, in each category
Examples
- Timbits consumed during meetings by old office mate (per meeting over the course of 20
weekly meetings)
- 8, 6, 4, 1, 5, 8, 9, 6, 5, 8, 5, 6, 2, 4, 8, 10, 6, 2, 5
How to do it
- Let’s pick a “data range”
• It must be inclusive of all possible scores
• (0-10)
- Aside: is this data nominal, ordinal, interval, or ratio?
• Ratio scale
X f
10 1
9 1
8 4
7 0
6 4
5 4
4 3
3 0
2 2
1 1
0 0 Some interesting things to note
- The X column is the scale of measurement, NOT the actual scores
• The X column is like a ruler
• It contains space enough for all possible raw scores in the sample
- Add up the ‘f’column
• What do you suppose is meant by the following question? f= N
• The sum of the frequency = the population size
Obtaining X from a frequency distribution table
X f
5 2
4 2
3 3
2 1
2 2
1
- Calculate X
• How many people got a score of 5? (2)
• How many people got a score of 4? (2)
• How many people got a score of 3? (3)
• How many people got a score of 2? (1)
• How many people got a score of 1? (2)
• X = 31 (X is multiplied by the frequency)
Obtaining X from a table
- With frequency distributions like this one: - X = Xf
• The sum of X = the sum of X multiplied by f
X f Xf
5 2 10
4 2 8
3 3 9
2 1 2
1 2 2
- Xf= 31
Proportions
- What is a ‘proportion’?
- Find proportion by count number of people who are asleep, and divide it by the number
of people in the class.
Proportions
- What proportion of people earned a score of 5?
X f
5 2
4 2
3 3
2 1
1 2
- How many people were measured in this study?
• N = f = 10
- What proportion of people earned a score of 5?
• .2
- So, what proportion of people earned a score of 5?
• Proportion = p = f/N
• = 2/10 = .2
Proportions
- What is p? (sum of the proportions) (add up all the p)
• The sum is 1
- You know you have done everything properly if the SUM OFTHE PIS
EQUALTO 1!!!
- No proportion can be higher than 1 and no proportion can be lower than 0
X f p = f/N
5 2 2 / 10 = .2
4 2 2 / 10 = .2
3 3 3 / 10 = .3 2 1 1 / 10 = .1
1 2 2 / 10 = .2
Percentages
- What percentage of people earned a score of 3?
X f
5 2
4 2
3 3
2 1
1 2
- %= p(100)
- = (f/N)(100)
- = (3/10) (100)
- = 300/10 (or .3(100))
- = 30
- 30% means that for every 100 people, 30 have the score in this frequency category
Proportions
- What is %?
X f % = p(100)
5 2 .2(100) = 20
4 2 .2(100) = 20
3 3 .3(100) = 30
2 1 .1(100) = 10
1 2 .2(100) = 20
- The sum of the percentage must be between 0 and 100%
Aproblem...
- Imagine I had 200 students, all with marks on a test ranging from 50 to 99
- The mark represents ‘number of correct responses’on a test with 99 questions
- How many rows would my frequency distribution have if I included all possible mark
results?
• That is: how many ‘X’categories would there be?
• Hint: This is a ratio scale
Grouped frequency distribution tables
- Sometimes there is just too much variability in the raw data to allow you to have a
simple, single-digit x-column ‘ruler’
- So how do instructors cope with this sort of thing? Consider the following
- Only 10 categories to manage
- It’s easy to see what is happening here
X f
95 – 99 17
90 – 94 15
85 – 89 19
80 – 84 11
75 – 79 4
70 – 74 6
65 – 69 7
60 – 64 3
55 – 59 4
50 – 54 14
- W

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