Question

Construction of a cumulative frequency table is useful in determining the
(a) Mean
(b) Median
(c) Mode
(d) All the above measurements

Answer 1

Hint: To solve this question, we will consider all the options separately one by one and consider the definition of the mean, median and mode. The definition which has cumulative frequency required inside it will have the answer here.

Complete step by step answer:
Let us first define the cumulative frequency. 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.
Now, consider option (a), the mean is the average of the numbers. Therefore, the mean of some terms of a frequency table can be determined by using the formula,
\[\text{Mean}=\dfrac{\text{Sum of the terms}}{\text{Number of terms}}\]
Clearly, by observing this formula, we see that there is no mention of the cumulative frequency table in the determination of the mean.
Therefore, option (a) Mean is not the right answer.
Now, let us consider the option (b).
Median: The median is the middle number in a sorted, ascending or descending order.
Now, we need ordered data to do that. Hence the median requires cumulative frequency because it provides us the ordered data whether ascending or descending.
Hence, option (b) is the right answer.
\[\text{Median for a grouped data}=\left\{ \begin{align}
  & {{\left( \dfrac{n+1}{2} \right)}^{th}}\text{ term if n is odd} \\
 & {{\left( \dfrac{n}{2}+1 \right)}^{th}}\text{ term if n is even} \\
\end{align} \right.\]
Now, let us consider the option (c).
Mode: The mode is the value that appears most frequently in a data set. Clearly, as observed by the definition of mode, we can say that mode doesn’t use the cumulative frequency.
Hence, the option (c) is wrong.

So, the correct answer is “Option B”.

Note: There are two types of median: Median of a grouped data or that of an ungrouped data. Usually, cumulative frequency is required for determining the median of ungrouped data although it can be used for grouped data as well when the frequency is stated.