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Histogram


 

A histogram is graphic representation of the frequency distribution of a continuous variable. Rectangles are drawn in such a way that their bases lie on a linear scale representing different intervals, and their heights are proportional to the frequencies of the values within each of the intervals.
 

Example :

Given below is a frequency table and the corresponding histogram showing the number of employees in a particular factory, according to their income.
 

Solution :
 

Frequency table showing 100 employees in a factory, according to their income level

Income levels
(rupees)
Tally marks Frequency
0 - 449 || 12
500 - 999 || 12
1000 - 1499 | 11
1500 - 1999 5
2000 - 2499 ||| 18
2500 - 2999 |||| 19
3000 - 3499 || 12
3500 - 3999 |||| 9
4000 - 4499 || 2
Total   100
 


Answer the following questions : -
 

Question

What is the class interval?

Solution

(Ans. 500)

 

Question

In which income group do the bulk of employees lie?

Solution

(Ans. Rs.2500 – Rs.2999)

 

Example

Why has a non-overlapping interval been chosen?

Solution

(Ans. Because the data is discrete.)

 

Example

Which group has the minimum number of employees? Why?  

Solution

(Ans. Rs.4000 – Rs.4499 i.e. the highest income group. Only very senior people are there in this group. The number of such people is usually very small.)

 

If you have a good look at the histogram given above, you will notice that:
 

1. A histogram looks like a bar graph, but there is no space between one bar and the other.


2. The histogram has a title.
 

3. On the

X-axis, the class intervals of the grouped data are shown. What the distribution depicts is also written below it.


4. On the

Y-axis, the frequencies for each class interval are shown.


5. On both the axes, suitable scales are taken.


6. The heights of the rectangles drawn are proportional to the frequencies of their classes.  

 

The weights of 30 students in a class (in kg) are as follows
42, 52, 46, 63, 47, 40, 50, 63, 52, 57, 40,47, 55, 52, 49, 42, 56, 51, 48, 47, 44, 54, 54, 62, 60, 58, 56, 60, 58, 53

Prepare a frequency distribution and draw a histogram, taking a suitable class interval. 

 

Answer the following questions : -
 

Example

If students of this age-group under 45 kg are considered underweight, what percentage of them are underweight?

(i) What weight range do most students lie in?

(ii) If students with weights of 60 kg or more are not considered for training in athletics, how many would get rejected?

Solution

We choose a class interval of 5. There will be 5 classes, which is convenient to handle.
 

Weight (kg) Tally marks Frequency
40 - 45 5
45 - 50 | 6
50 - 55 ||| 8
55 - 60 | 6
60 - 65 5
Total   30

Notice that since the first class interval starts at 40 kg, and not from 0, we give a break indicated by  (Kink) between 0 and 40.

(i) Percentage of underweight student = 5/30 × 100% = 16.67%.

(ii) 50 kg - 55 kg.

(iii) 5 students in the 60 kg - 65 kg class. So, 5 students would get rejected.

 




 





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