Question

Present the data given in the table below in the form of a Histogram :

Mid-points	:	115	125	135	145	155	165	175	185	195
Frequency	:	6	25	48	72	116	60	38	22	3

Answer 1

The two-dimensional diagrams that depict the frequency distribution of a continuous series by the means of rectangles are called histograms.
In order to construct a histogram, we first require the class intervals corresponding to the various mid-points, which is calculated using the following formula.

The value obtained is then added to the mid point to obtain the upper limit and subtracted from the mid-point to obtain the lower limit.

For the given data, the class interval is calculated by the following value of adjustment.
$\mathrm{Value}\mathrm{of}\mathrm{Adjustment}=\frac{125-115}{2}=5$

Thus, we add and subtract 5 to each mid-point to obtain the class interval.

For instance:

The lower limit of first class = 115 – 5 = 110

Upper limit of first class = 115 + 5 = 120.

Thus, the first class interval is (110-120). Similarly, we can calculate the remaining class intervals.

Mid-points	Class Interval	Frequency
115 125 135 145 155 165 175 185 195	110 − 120 120 − 130 130 − 140 140 − 150 150 − 160 160 − 170 170 − 180 180 − 190 190 − 200	6 25 48 72 116 60 38 22 3