Frequency Distribution
|
Class Interval |
Frequency |
Class Midpoint |
Relative Frequency |
Cumulative Frequency |
|
6.30-under 6.50 |
1 |
6.40 |
.0167 |
1 |
|
6.50-under 6.70 |
3 |
6.60 |
.0500 |
4 |
|
6.70-under 6.90 |
12 |
6.80 |
.2000 |
16 |
|
6.90-under 7.10 |
18 |
7.00 |
.3000 |
34 |
|
7.10-under 7.30 |
16 |
7.20 |
.2666 |
50 |
|
7.30-under 7.50 |
9 |
7.40 |
.1500 |
59 |
|
7.50-under 7.70 |
1 |
7.60 |
.0167 |
60 |
|
Totals |
60 |
7.80 |
1.0000 |
|
Solution in Detail
Construct a Frequency Distribution
a) Determine the range (difference between the largest and smallest numbers)
b) Determine how many classes it will contain. Between 5 and 15 classes is recommended.
c) Determine the width of the class interval. Divide the range by the total number of classes.
Range: 7.56 – 6.35 = 1.21
# Of Classes: We choose 7
Class Width: 1.21 / 7 = 0.173
Perhaps, round up Class Width to 0.20. Use that to determine the 7 Class Intervals.
|
Interval |
Frequency |
Class Midpoint |
Relative Frequency |
Cumulative Frequency |
|
6.30-under 6.50 |
|
|
|
|
|
6.50-under 6.70 |
|
|
|
|
|
6.70-under 6.90 |
|
|
|
|
|
6.90-under 7.10 |
|
|
|
|
|
7.10-under 7.30 |
|
|
|
|
|
7.30-under 7.50 |
|
|
|
|
|
7.50-under 7.70 |
|
|
|
|
|
Totals |
|
|
|
|
Now determine the Frequency. Do we simply count? Yes, remember that the frequency (f) of a particular observation is the number of times the observation occurs in the data. There is only one number between 6.30 and 6.50: 6.35. Therefore the frequency of that class interval is 1. In the same way, fill the rest of the rows in the Frequency column.
