Question

Construct a frequency distribution table for the following weights (in grams) of 35 mangoes, using the equal class intervals, one of them is 40 – 45 (45 not included).
30, 40, 45, 32, 43, 50, 52, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68
A. How many classes are there in the frequency distribution table?
B. Which weight group has the highest frequency?

Answer 1

Here to construct the frequency distribution table, we need to find the lowest class interval and highest class interval first. So, find the smallest and greatest weights from the given weights and that will give you the first and last class intervals of the frequency distribution table. The size of each class interval must be 5. After finding the first and last class intervals, draw the frequency distribution table with the required class intervals. Now, insert all the weights in the table according to their class intervals.

Complete step-by-step answer:
In this question, we are given 35 weights of mangoes and we have to construct a frequency distribution table for it.
Here, it is mentioned that we have to use equal class intervals that is 5.
Now, to find the first class interval and last class interval find the smallest weight and the largest weight from the given weights.
Here,
$\Rightarrow$Smallest weight$= 30$
$\Rightarrow$Largest weight$= 74$
Hence, the first class interval will be 30 – 35 and the last class interval will be 70 – 75.
Let us make a frequency distribution table for this.

Class Intervals (Weight)	Frequency (No of Mangoes)
30 – 35	4
35 – 40	1
40 – 45	3
45 – 50	3
50 – 55	7
55 – 60	3
60 – 65	6
65 – 70	5
70 – 75	3

A. How many classes are there in the frequency distribution table?
$\Rightarrow$There are 9 class intervals in this frequency distribution table

B. Which weight group has the highest frequency?
$\Rightarrow$ If we look at the frequency column, the highest frequency is 7 and the class interval of 7 is 50 – 55.

Note: Here, note that as the class interval is continuous, the extreme value of lower limit is included in the same class interval. Lower limit means the lowest number in the class interval.
For example: Note that we have included the weight in class interval 30 – 35.
The difference between continuous class interval and discontinuous class interval is that in continuous, the Higher Limit of first interval is equal to the lower limit of the second interval. In discontinuous, the lower limit of the second interval precedes the higher limit of previous interval by 1.
Example of Continuous class interval: 5 – 10, 10 – 15
Example of Discontinuous class interval: 1 – 5, 6 – 11