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Question

# Find the median for the given data by drawing a 'less than ogive': [6 MARKS] Class interval0−1010−2020−3030−4040−50Frequency4915148

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Solution

## Formula: 2 Marks Table: 2 Marks Graph: 2 Marks To draw the 'less than ogive', first we prepare the cumulative frequency table as given below: ObservationsFrequencyObservationsCumulative frequency(in classes)(in ′less than′ form)0−104Less than 10410−209Less than 201320−3015Less than 302830−4014Less than 404240−508Less than 5050 Now, we mark the upper class limits along the x-axis on a suitable scale and the corresponding cumulative frequencies along the y-axis on a suitable scale. We plot the points (0, 0), (10, 4), (20, 13), (30, 28), (40, 42) and (50, 50). We join the plotted points by a freehand curve to obtain the required ogive as shown below. Total no. of observations = n = 50. To find the median from this ogive, first we locate the number n2=502=25 on the y-axis. From the point marked 25 on they-axis, we draw a horizontal line parallel to the x-axis intersecting the ogive at point A. From the point A, we draw a vertical line perpendicular to the x-axis meeting it at B. The value of point B on x-axis is 28. Hence, the required median is 28.

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