Question

The class intervals in a frequency distribution are:
40 – 44, 45 – 49, 50 – 54,........ If the frequency distribution, is converted into a continuous frequency distribution then the class intervals are _________.

Answer 1

If a–b is a class in inclusive method, then in exclusive method the corresponding class is $\left(a-\frac{h}{2}\right)$–$\left(b+\frac{h}{2}\right)$, where h = $\frac{1}{2}$(Lower limit of a class − Upper limit of previous class).

In the given class intervals, the difference between the lower limit of a class and upper limit of the previous class is 1. Here, h = $\frac{1}{2}$ = 0.5.

So, we subtract 0.5 from the lower limit of each class and add 0.5 in the upper limit of each class to make it continuous.

For the class 40–44, the corresponding class is (40 − 0.5)–(44 + 0.5) i.e. 39.5–44.5

For the class 45–49, the corresponding class is (45 − 0.5)–(49 + 0.5) i.e. 44.5–49.5

For the class 50–54, the corresponding class is (50 − 0.5)–(54 + 0.5) i.e. 49.5–54.5 and so on

Thus, the class intervals in the continuous frequency distribution are 39.5–44.5, 44.5–49.5, 49.5–54.5, ... .

The class intervals in a frequency distribution are: 40 – 44, 45 – 49, 50 – 54,........ If the frequency distribution, is converted into a continuous frequency distribution then the class intervals are ___39.5–44.5, 44.5–49.5, 49.5–54.5, ...___.