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Question
Draw a cumulative frequency curve more than type for the following data and hence locate Q1 and Q3. Also, find the number of workers with daily wages
(i) Between ₹ 170 and ₹ 260
(ii) less than ₹ 260
| Daily wages more than (₹) | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 |
| No. of workers | 200 | 188 | 160 | 124 | 74 | 49 | 31 | 15 | 5 |
Solution
For more than ogive points to be plotted are (100, 200), (150, 188), (200, 160), (250, 124), (300, 74), (350, 49), (400, 31), (450, 15), (500, 5)
Here, N = 200
For Q1, `"N"/4=200/4` = 50,
For Q3, `(3"N")/4-(3xx200)/4` = 150
We take the points having Y co-ordinates 50 and 150 on Y-axis. From these points, we draw lines that are parallel to X-axis. From the points of intersection of these lines with the curve, we draw perpendicular on X-axis. X-Co-ordinates of these points gives the values of Q1 and Q3.
Since X-axis has daily wages more than and not less than the given amounts.
∴ Q1 = Q3 and Q3 = Q1
∴ Q1 ≈ 215, Q3 ≈ 348
(i) To find the number of workers with daily wages between ₹ 170 and ₹ 260,
Take the values 170 and 260 on X-axis. From these points, we draw lines parallel to Y-axis. From the point where they intersect the more than ogive, we draw perpendiculars on Y-axis.
The points where they intersect the Y-axis gives the values 178 and 114.
∴ Number of workers having daily wages between ₹ 170 and ₹ 260 = 178 – 114 = 64
(ii) To find the number of workers having daily wages less than ₹ 260, we consider the value 260 on the X-axis. From this point, we draw a line that is parallel to Y-axis. From the point where the line intersects the more than ogive, we draw a perpendicular on the Y-axis. Foot of perpendicular gives the number of workers having daily wages more than 260.
Foot of perpendicular ≈ 114
∴ No. of worker whose daily wages more than ₹ 260 ≈ 114
∴ No. of workers whose daily wages less than ₹ 260 = 200 – 114 = 86
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