The heights (to the nearest inch) of 30 males are shown below. Construct a frequency distribution and a frequency histogram of the data using 5 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.
The heights (to the nearest inch) of 30 males are shown below. Construct a frequency distribution and a frequency histogram of the data using 5 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.
|
67
|
76
|
69
|
68
|
74
|
|
|
68
|
65
|
63
|
75
|
69
|
|
|
66
|
72
|
66
|
66
|
69
|
|
|
73
|
62
|
62
|
71
|
73
|
|
|
70
|
72
|
71
|
65
|
69
|
|
|
66
|
74
|
72
|
68
|
69
|
|
Class
|
Frequency
|
Midpoint
|
|---|---|---|
|
nothing–nothing
|
nothing
|
nothing
|
|
nothing–nothing
|
nothing
|
nothing
|
|
nothing–nothing
|
nothing
|
nothing
|
|
nothing–nothing
|
nothing
|
nothing
|
|
nothing–nothing
|
nothing
|
nothing
|
Here,
The smallest value of the dataset=62
The largest value of the dataset=76
The range of the data set is thus obtained as-
The class width for the frequency distribution for 5 classes is obtained as-
The lower class limit for the frequency distribution is obtained as-
|
62 62+3=65 65+3=68 68+3=71 71+3=74 |
The upper class limits for the frequency distribution is obtained as-
|
62+(3-1)=64 65+(3-1)=67 68+(3-1)=70 71+(3-1)=73 74+(3-1)=76 |
The required frequency distribution of the data using 5 classes is obtained as-
| Class | Frequency | Mid-point |
| 62-64 | 3 | 63 |
| 65-67 | 7 | 66 |
| 68-70 | 9 | 69 |
| 71-73 | 7 | 72 |
| 74-76 | 4 | 75 |
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