We will discuss here some of the problems on histogram.

1. The histogram for a frequency distribution is given below.

Answer the following.

(i) What is the frequency of the class interval 15 – 20?

(ii) What is the class intervals having the greatest frequenciey?

(iii) What is the cumulative frequency of the class interval 25 – 30?

(iv) Construct a short frequency table of the distribution.

(v) Construct a cumulative frequency table of the distribution.

**Solution:**

(i) 25

(ii) 20 – 25

(iii) 90

(iv)

10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 |
20 25 30 15 10 5 |

(v)

10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 |
20 25 30 15 10 5 |
20 45 75 90 100 105 |

**2.** The histogram for a frequency distribution is as shown
below.

Answer the following.

(i) Find the class intervals having the greatest and the least frequencies.

(ii) Find the class interval whose frequency is 40.

(iii) What is the frequency of the class interval 30 – 40?

(iv) What is the cumulative frequency of the class interval 30 – 40?

(v) Construct the frequency table of the distribution.

**Solution:**

(i) The class interval 10 – 20 has the greatest frequency as the rectangle corresponding to the interval has the greatest area, the height being the greatest.

(ii) 20 – 30

(iii) 30

(iv) 50 + 40 + 30 = 120

(v)

**Class Interval**

10- 20

20 - 30

30 - 40

40 - 50

**Frequency**

50

40

30

40

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