Maharashtra State BoardHSC Commerce 11th
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Draw ogive for the Following distribution and hence find graphically the limits of weight of middle 50% fishes. Weight of fishes (in gms) 800 – 890 900 – 990 1000 – 1190 1100 – 1090 1200 – - Mathematics and Statistics

Graph

Draw ogive for the Following distribution and hence find graphically the limits of weight of middle 50% fishes.

Weight of fishes (in gms) 800 – 890 900 – 990 1000 – 1090 1100 –  1190 1200 – 1290 1300 –1390 1400 – 1490
No. of fishes 8 16 20 25 40 6 5
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Solution

Since the given data is not continuous, we have to convert it in the continuous form by subtracting 5 from the lower limit and adding 5 to the upper limit of every class interval. To draw a ogive curve, we construct the less than cumulative frequency table as given below:

Weight of fishes
(in gms)
No. of fishes
(f)
Less than cumulative frequency
(c.f.)
795 – 895 8 8
895 – 995 16 24
995 – 1095 20 44
1095 – 1195 25 69
1195 – 1295 40 109
1295 – 1395 6 115
1395 – 1496 5 120
Total 120  

Points to be plotted are (895, 8), (995, 24),(1095, 44),(1195, 69),(1295, 109), (1395, 115), (1495, 120).

N = 120 

For Q1 and Q3 we have to consider `"N"/4=120/4` = 30, `(3"N")/4=(3xx120)/4` = 90

For finding Q1 and Q3 we consider the values 30 and 90 on the Y-axis. From these points, we draw the lines which are parallel to X-axis. From the points where these lines intersect the less than ogive, we draw perpendicular on X-axis. The feet of perpendiculars represent the values of Q1 and Q2.

∴ Q1 ≈ 1025 and Q3 ≈ 1248

∴ The limits of weight of middle 50% fishes lie between 1025 to 1248.

Concept: Graphical Location of Partition Values
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