Question

Consult a frequency table with class interval of $5$ for the following data:
\[2,4,8,11,14,16,20,28,25,40,30,48,5,22,29,13,22,17,17,7\]

Answer 1

Hint: From the question, we have to consider a frequency table with class interval $5$ for the given data set. We need to find the range of the given data set first to proceed for constructing the class intervals. The dataset needs to be arranged properly to find out the range.

Formula used: We will calculate the range first.
Range= ${\text{Maximum value - minimum value}}$

Complete step-by-step solution:
 The entire data set needs to be arranged in ascending order to find out the maximum and minimum values easily.
\[2,4,5,7,8,11,13,14,16,17,17,20,22,22,25,28,29,30,40,48\]
Maximum value= $48$
Minimum value= $2$
Here we have to construct the frequency table we must know the range of the data set. So,
Range=${\text{Maximum value - minimum value}}$
Putting the values and we get,
$ \Rightarrow 48 - 2$
On subtracting we get,
$ \Rightarrow 46$
Now we have to make $5$ class intervals, that is, we need to divide the range in $5$ equal parts.
But $46$ is not divisible by $5$
So, we take $50$ as the range and divide it into $5$ equal parts.
So, the ranges will be $1 - 10,11 - 20,21 - 30,31 - 40,41 - 50$.
Frequency is the number of occurrences of an observation.
Here, the frequency column will be the count of observations that are in the class interval, that is, in the range of $1 - 10$, there are \[2,4,5,7,8\] that is $5$ values.
So, the frequency of this class interval is $5$.

Class Interval	Frequency
$1 - 10$	$5$
$11 - 20$	$7$
$21 - 30$	$6$
$31 - 40$	$1$
$41 - 50$	$1$
Total	$20$

This is the frequency table for the given dataset.

Note: Frequency table is a very important part of data presentation. It helps to tabulate the raw, clustered data in a systematic and organized way. It helps one to understand the groupings of the data easily. Class intervals help to obtain the required data faster with a glance.