Question

In a frequency distribution with classes $0 - 10,10 - 20$ and so on, the size of class interval is 10. What is the lower limit of the fourth class?
A) $40$
B) $50$
C) $20$
D) $30$

Answer 1

Hint: In this question, we are given the first two classes of a frequency distribution and the size of the class interval. We have to find out the lower limit of the fourth class. Start by finding the classes of the given frequency distribution using the class size and then count which is the fourth class. And then choose its lower limit from the options.

Complete step-by-step solution:
We are given two classes of the frequency distribution and we are also given the size of those intervals. We have been asked the lower limit of the fourth class. But first, let us know what is lower and upper limit, and what is class size.
Lower limit is the least value of the data that can be counted in a particular group and upper limit is the highest value of the data that can be considered in that group. For example: for class limits $0 - 10$, $0$ is the lower limit and $10$ is the upper limit.
When we subtract the lower limit from the upper limit, we get the class size. For example: for class limit $0 - 10$, class size $ = 10 - 0 = 10$.
Now, let us move towards the question.
We have $0 - 10,10 - 20$. We can form the class intervals after this,
$1^{st}$ class interval$ = 0 - 10$
$2^{nd}$ class interval$ = 10 - 20$
$3^{rd}$ class interval$ = 20 - 30$
$4^{th}$ class interval$ = 30 - 40$
$5^{th}$ class interval$ = 40 - 50$
And so on, …

$\therefore $ Our $4^{th}$ class interval $ = 30 - 40$. Its lower limit is option D) 30.

Note: We can observe that frequency distribution is statistics is a representation that displays the number of observations within a given interval. The representation of a frequency distribution can be graphical or tabular so that is easier to understand. Frequency distributions are particularly useful for normal distributions, which show the observations of probabilities divided among standard deviation. In finance, traders use frequency distributions to take note of price action and identify trends.