We will discuss here some of the problems on frequency polygon.

**1.** The frequency polygon of a frequency distribution is
shown below.

Answer the following about the distribution from the histogram.

(i) What is the frequency of the class interval whose class mark is 15?

(ii) What is the class interval whose class mark is 45?

(iii) Construct a frequency table for the distribution.

**Solution:**

(i) 18

(ii) 40 – 50

(iii) As the class marks of consecutive overlapping class intervals are 5, 15, 25, 35, 45, 55 we find the class intervals are 0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50, 50 – 60. Therefore, the frequency table is constructed as below.

0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 |
10 18 14 26 8 18 |

**2.** The following frequency polygon displays the weekly
incomes of laborers of a factory.

Answer the following.

(i) Find the class interval whose frequency is 25.

(ii) How many labourers have a weekly income of at least $ 500 but not more than $ 700?

(iii) What is the range of weekly income of the largest number of labourers?

(iv) Prepare the frequency distribution table.

**Solution:**

(i) The frequency 25 corresponds to the class mark 800.

The common width of class intervals = 400 - 200 = 200

So, the class interval is (800 - \(\frac{200}{2}\)) – (800 + \(\frac{200}{2}\)), i.e., 700 – 900

(ii) The number of labourers has to fall in the class interval 500 – 700 whose class mark is 600. The frequency corresponding to the class mark 600 is 20. Hence, the required number of labourers is 20.

(iii) The largest number of labourers belong to the class interval whose class mark is 400. The corresponding class interval is (400 - \(\frac{200}{2}\)) – (400 + \(\frac{200}{2}\)), i.e., (300 – 500). So, the largest numbers of labourers have a weekly income of at least $ 300 but less than $ 500.

(iv)

Weekly Income (in $)

100 - 300

300 - 500

500 - 700

700 - 900

Number of labourers

30

40

20

25

**From Problems on Frequency Polygon**

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