The electricity bills (in rupees) of 40 houses in a locality are given below :

78 87 81 52 59 65 101 108 115 95

98 65 62 121 128 63 76 84 89 91

65 101 95 81 87 105 129 92 75 105

78 72 107 116 127 100 80 82 61 118

Form a frequency distribution table with a class size of 10. Also represent the above data with a histogram and frequency polygon.

From data,

Least term = 52 and Greatest term = 129.

Range = Greatest term - Least term = 129 – 52 = 77.

Construct a frequency distribution table:

Steps of construction of histogram :

1. Since, the scale on x-axis starts at 40, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 40.

2. Take 1 cm along x-axis = 10 units.

3. Take 1 cm along y-axis = 2 units.

4. Construct rectangles corresponding to the above continuous frequency distribution table.

The required histogram is shown in the adjoining figure.

Steps of construction of frequency polygon :

1. Mark the mid-points of upper bases of rectangles of the histogram.

2. Join the consecutive mid-points by line segments.

3. Join the first end point with the mid-point of class 40 - 50 with zero frequency, and join the other end point with the mid-point of class 130 - 140 with zero frequency.

The required frequency polygon is shown by thick line segments in the diagram.