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Mathematics

Estimate the median for the given data by drawing ogive :

ClassFrequency
0 - 104
10 - 209
20 - 3015
30 - 4014
40 - 508

Measures of Central Tendency

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Answer

Cumulative frequency distribution table :

ClassFrequencyCumulative frequency
0 - 1044
10 - 20913 (4 + 9)
20 - 301528 (13 + 15)
30 - 401442 (28 + 14)
40 - 50850 (42 + 8)

Here, n = 50, which is even.

By formula,

Median = n2 th term=502\dfrac{n}{2}\text{ th term} = \dfrac{50}{2} = 25th term.

Steps of construction of ogive :

  1. Take 2 cm = 10 units on x-axis.

  2. Take 1 cm = 5 units on y-axis.

  3. Plot the point (0, 0), as ogive always starts on x-axis representing the lower limit of the first class.

  4. Plot the points (10, 4), (20, 13), (30, 28), (40, 42) and (50, 50).

  5. Join the points by a free hand curve.

  6. Draw a line parallel to x-axis from point A (frequency) = 25, touching the graph at point B. From point B draw a line parallel to y-axis touching x-axis at point C.

Estimate the median for the given data by drawing ogive. Measures of Central Tendency, Concise Mathematics Solutions ICSE Class 10.

From graph, C = 28.

Hence, median = 28.

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