Now we know about class interval, class limits, size of class interval, frequency distribution, class boundaries and mid class. On the basis of all these concepts, we are now able to construct a frequency distribution table with the help of problem A. 

Problem A: Using following data, construct a frequency distribution table of weight of 50 boys. Use 8 class intervals of equal size and also find class boundaries and mid class. 125, 108, 119, 115, 129, 140, 137, 130, 129, 124, 111, 100, 127, 130, 150, 96, 141, 122, 122, 136, 92, 124, 139, 109, 105, 114, 131, 124, 136, 132, 151, 127, 125, 123, 119, 124, 134, 129, 104, 102, 125, 148, 143, 124, 123, 101, 147, 100, 126, 131.

Solution

In order to construct a frequency distribution table, it is preferable to arrange the data in ascending or descending order so that one could easily judge the highest or lowest observation. In this case we will arrange the data in ascending order.
Ascending Order:

92, 96, 100, 100, 101, 102, 104, 105, 108, 109, 111, 114, 115, 119, 119, 122, 122, 123, 123, 124, 124, 124, 124, 124, 125, 125, 125, 126, 127, 127, 129, 129, 129, 130, 130, 131, 131, 132, 134, 136, 136, 137, 139, 140, 141, 143, 147, 148, 150, 151.

Step 1 Find the Range

Range = Largest Observation – Smallest Observation

Here,
Largest Observation = 151
Smallest Observation = 92
Therefore Range = 151 – 92 = 59

Step 2 Find the Size of Class Interval

From the problem we know that there are 8 class intervals and we have to use class intervals of equal size. We also know that the range for the given data is 59. So in order to find the size of class interval the formula will be

Size of class interval = Range/ Total no of class intervals
Size of class interval = 59/8 = 7.375 = 8 approx (note: in case the fraction appears, the next higher whole number is usually taken as the size of the class interval).

Step 3 Prepare a Tally Sheet

 Tally Sheet

In the above table, first column shows class intervals for the weight of 50 boys. The first class interval should be started with the nearest round number below the minimum value of the data. In this case, minimum value is 92 therefore we started the first interval from 91. The second column labeled Tally shows the number of tallies in each interval. For example only two observations (92, 96) fall in the first class interval (91 – 98) therefore it will be shown by two straight lines under the column Tally. In order to make counting of the tallies simple, tallies are put in groups of five. The number of tallies in each interval is the frequency of that interval as shown in the third column labeled frequency.

Step 4 Construct Frequency Distribution Table

In order to construct frequency distribution table just remove the tally column from the above table. And after that further calculation such as class boundaries and Mid. class can be done easily.

Frequency Distribution Table