Question

A grouped frequency distribution table with classes of equal size, using 63-72 (72 included) as one of the classes, is constructed for the following data:
30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96, 102, 110, 88, 74, 112, 14, 34, 44
The number of classes in the distribution will be __________.

Answer 1

The given class is 63–72 (72 is included in the same class). So, the frequency distribution is to be formed by inclusive method.

Size of each class interval = 10 (72 is included in the given class)

Highest value of the observations = 112

Lowest value of the observations = 14

∴ Range of the data = Highest value of the observations − Lowest value of the observations = 112 − 14 = 98

Now,

$\frac{\mathrm{Range}\mathrm{of}\mathrm{the}\mathrm{data}}{\mathrm{Size}\mathrm{of}\mathrm{each}\mathrm{class}\mathrm{interval}}=\frac{98}{10}$ = 9.8

So, the number of classes of equal size in the distribution will be 10. The class in the distribution are

13–22, 23–32, 33–42, 43–52, 53–62, 63–72, 73–82, 83–92, 93–102, 103–112

Thus, the number of classes in the distribution is 10.

The number of classes in the distribution will be ___10___.