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.