3. Frequency and Percentage Distribution
Used to determine the percentage usually for data on
profile (e.g. level, age, gender, etc.)
% =
𝑓
𝑁
𝑥 100
where:
% - percentage
f – frequency or number of
respondents for every item
N - total no. of respondents
P =
𝑓
𝑁
𝑥 100%
where:
P - percentage
f – frequency or number of
respondents for every item
N - total no. of respondents
4.
5.
6.
7. Weighted mean
Used to get the average or central value (e.g. level,
extent, status, etc.)
𝒙 =
𝒇𝒙
𝒏
where:
𝒙 - weighted mean
f – the frequency of scores
n - number of respondents
8.
9.
10.
11.
12.
13.
14. Measures of Position
Ungrouped data
Also known as Measures of Location. These are
identified as values which divides the data set into a
desired equal parts.
4 parts – Quartile
10 parts – Decile
100 parts - Percentile
21. Special Similarities
Measures of Position is directly connected
with Measures of Central Tendency.
The 5th decile, the 50th percentile are equal
to the median.
26. Quartile
Average of the
𝑥𝑁
4
𝑡ℎ and
𝑥𝑁
4
+ 1 𝑡ℎ term
𝑪𝒂𝒔𝒆 𝟑.
N is an even number.
𝑁 is divisible by 4.
67, 69, 70, 71, 72, 74, 75, 77, 79, 80, 82, 83, 84, 87, 89, 91
𝑄1
1
4
16
4𝑡ℎ
71
𝟕𝟏. 𝟓
1
4
16 + 1
5𝑡ℎ
72
71 + 72
2
71.5
𝑄2
1
2
16
8𝑡ℎ
77
1
4
16 + 1
5𝑡ℎ
79
77 + 79
2
78
𝟕𝟖
Average of the
𝑥
4
(𝑁) and
𝑥
4
𝑁 + 1
27. Quartile
Average of the
𝑥𝑁
4
𝑡ℎ and
𝑥𝑁
4
+ 1 𝑡ℎ term
𝑪𝒂𝒔𝒆 𝟑.
N is an even number.
𝑁 is divisible by 4.
67, 69, 70, 71, 72, 74, 75, 77, 79, 80, 82, 83, 84, 87, 89, 91
𝑄3
3
4
16
12𝑡ℎ
83
𝟖𝟑. 𝟓
3
4
16 + 1
13𝑡ℎ
84
83 + 84
2
𝟖𝟑. 𝟓
Average of the
𝑥
4
(𝑁) and
𝑥
4
𝑁 + 1
28. Quartile
𝑪𝒂𝒔𝒆 𝟒.
N is an even number.
𝑁 is not divisible by 4.
Average of the
1
2
𝑁 𝑡ℎ and
1
2
𝑁 + 1 𝑡ℎ term
Second Quartile
𝑥
4
𝑁 + 0.5 𝑡ℎ term
First and Third Quartile
67, 69, 71, 72, 74, 75, 77, 79, 80, 82, 83, 84, 85, 87, 89, 91, 93, 95
29. Quartile
𝑪𝒂𝒔𝒆 𝟒.
N is an even number.
𝑁 is not divisible by 4. 𝑥
4
𝑁 + 0.5 𝑡ℎ term
First and Third Quartile
67, 69, 71, 72, 74, 75, 77, 79, 80, 82, 83, 84, 85, 87, 89, 91, 93, 95
𝑄1
1
4
18 + 0.5
5𝑡ℎ
74
𝑄3
3
4
18 + 0.5
14𝑡ℎ
87
30. Quartile
𝑪𝒂𝒔𝒆 𝟒.
N is an even number.
𝑁 is not divisible by 4.
Average of the
1
2
𝑁 𝑡ℎ and
1
2
𝑁 + 1 𝑡ℎ term
Second Quartile
67, 69, 71, 72, 74, 75, 77, 79, 80, 82, 83, 84, 85, 87, 89, 91, 93, 95
𝑄1
1
4
18 + 0.5
5𝑡ℎ
74
𝑄3
3
4
18 + 0.5
14𝑡ℎ
87
𝑄2
1
2
18
9𝑡ℎ
80
𝟖𝟏
1
2
18 + 1
10𝑡ℎ
82
80 + 82
2
81
31.
32. Quartile
𝑄𝑥 =
𝑥
4
(𝑛 + 1)
𝑪𝒂𝒔𝒆 𝟏.
N is an odd number.
𝑁 + 1 is divisible by 4.
𝑪𝒂𝒔𝒆 𝟐.
N is an odd number.
𝑁 + 1 is not divisible by 4.
33. Quartile
𝑪𝒂𝒔𝒆 𝟑.
N is an even number.
𝑁 is divisible by 4.
Average of the
𝑥
4
(𝑁) and
𝑥
4
𝑁 + 1
𝑪𝒂𝒔𝒆 𝟒.
N is an even number.
𝑁 is not divisible by 4.
Average of the
1
2
𝑁 𝑡ℎ and
1
2
𝑁 + 1 𝑡ℎ term
Second Quartile
𝑥
4
𝑁 + 0.5 𝑡ℎ term
First and Third Quartile