bus-stat-book1

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Unformatted text preview: 0.5 9 81 HISTOGRAM 35 Number of Students 30 25 20 15 10 5 0 20.5 30.5 40.5 50.5 60.5 70.5 80.5 Marks Example 12: Draw a histogram for the following data. Profits Number of (in lakhs) Companies 0-10 4 10-20 12 20-30 24 30-50 32 50-80 18 80-90 9 90-100 3 Solution: When the class intervals are unequal, a correction for unequal class intervals must be made. The frequencies are adjusted as follows: The frequency of the class 30-50 shall be divided by two since the class interval is in double. Similarly the class interval 5080 can be divided by 3. Then draw the histogram. 82 Now we rewrite the frequency table as follows. Profits (in lakhs) 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Number of Companies 4 12 24 16 16 6 6 6 9 3 HISTOGRAM 30 No. of Companies 25 20 15 10 5 0 10 20 30 40 50 60 Profits (in Lakhs) 5.6.2 70 80 90 100 Frequency Polygon: If we mark the midpoints of the top horizontal sides of the rectangles in a histogram and join them by a straight line, the figure so formed is called a Frequency Polygon. This is done under the assumption that the frequencies in a class interval are evenly distributed throughout the class. The area of the polygon is equal to the area of the histogram, because the area left outside is just equal to the area included in it. 83 Example 13: Draw a frequency polygon for the following data. Number of Students 4 7 10 18 14 8 3 Weight (in kg) 30-35 35-40 40-45 45-50 50-55 55-60 60-65 FREQUENCY POLYGON 20 18 Number of Students 16 14 12 10 8 6 4 2 0 30 35 40 45 50 55 60 65 Weight (in kgs) 5.6.3 Frequency Curve: If the middle point of the upper boundaries of the rectangles of a histogram is corrected by a smooth freehand curve, then that diagram is called frequency curve. The curve should begin and end at the base line. 84 Example 14: Draw a frequency curve for the following data. Monthly Wages (in Rs.) 0-1000 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000 6000-7000 7000-8000 No. of family 21 35 56 74 63 40 29 14 Solution: FREQUENCY CURVE 80 70 No. of Family 60 50 40 30 20 10 0 1000 2000 3000...
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