By taking classes 30 - 40, 40 - 50, 50 - 60, ……………, construct a frequency table for the following data :

65	34	74	49	52	35
71	55	61	40	56	38
52	56	52	33	60	35
49	37	53	50	44	30
62	50	47	45	47	50
63	61	54	58	47	64
37	38	44	42	47	55
70	33	75	49	47	30
60	69

Also, construct a combined histogram and frequency polygon for the distribution.

The frequency table for the given distribution is :

Steps:

1. Draw a histogram.

• On the x-axis, mark the class intervals: 30-40, 40-50, 50-60, 60-70 and 70-80.
• On the y-axis, mark the frequency values.
• Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.
• Since the scale on x-axis starts at 30, a kink (break) or a zig-zag curve is shown near the origin to indicate that the graph is drawn to scale beginning at 30 and not at the origin itself.

2. Mark the mid-points at the top of each rectangle of the histogram drawn.

• 30−40 → 35
• 40−50 → 45
• 50−60 → 55
• 60−70 → 65
• 70−80 → 75

3. Also, mark the mid-point of the immediately lower class-interval ( in the given example, the immediately lower class-interval is 20-30) and mid-point of the immediately higher class-interval (in the given example the immediate upper class-interval is 80-90).

4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.