Question

The cumulative frequency of the largest observed value must always be
(a) Less than the total number of observations
(b) Greater than the total number of observations
(c) Equal to the total number of observations
(d) Equal to the midpoint of the last class interval

Answer 1

Hint: To solve this question, we will first of all define the cumulative frequency. Then after that, we will take a simple example to check whether at which point the largest observed value of cumulative frequency is observed, that will be our final answer.

Complete step by step answer:
We know that the median requires cumulative frequency for its determination. Let us first define the cumulative frequency first. The Cumulative frequency analysis is the analysis of the frequency of occurrence of the values of a phenomenon less than a reference value. The cumulative frequency is also called the frequency of the non – exceedance.
For example, if some terms are given with some frequency then the cumulative frequency is determined as

Terms	Frequency	Cumulative
1	2	2
2	5	5 + 2 = 7
3	4	7 + 4 = 11
4	2	11 + 2 = 13
5	1	13 + 1 = 14

So, this is how cumulative frequency is determined. We see from the above stated example of cumulative frequency that the final value at the fifth term of the cumulative frequency is 14. That means 14 is the value at the last of the fifth term.
Hence, we can determine that the cumulative frequency of the largest observed value must be the last term in every case. And the last term equals the total number of observations. Here, the cumulative frequency of the largest observed value must always be equal to the total number of observations.

So, the correct answer is “Option C”.

Note: A possibility of mistake can be determining or involving in the median while going for the cumulative frequency distribution. This may change the answer as the median may not always be determined at last term, it can be middle term as well. So, always remember that the cumulative frequency doesn’t depend on the median, in fact, the median depends on the cumulative frequency.