Mathematics
Estimate the median for the given data by drawing ogive :
Class | Frequency |
---|---|
0 - 10 | 4 |
10 - 20 | 9 |
20 - 30 | 15 |
30 - 40 | 14 |
40 - 50 | 8 |
Measures of Central Tendency
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Answer
Cumulative frequency distribution table :
Class | Frequency | Cumulative frequency |
---|---|---|
0 - 10 | 4 | 4 |
10 - 20 | 9 | 13 (4 + 9) |
20 - 30 | 15 | 28 (13 + 15) |
30 - 40 | 14 | 42 (28 + 14) |
40 - 50 | 8 | 50 (42 + 8) |
Here, n = 50, which is even.
By formula,
Median = = 25th term.
Steps of construction of ogive :
Take 2 cm = 10 units on x-axis.
Take 1 cm = 5 units on y-axis.
Plot the point (0, 0), as ogive always starts on x-axis representing the lower limit of the first class.
Plot the points (10, 4), (20, 13), (30, 28), (40, 42) and (50, 50).
Join the points by a free hand curve.
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.](https://cdn1.knowledgeboat.com/img/cm10/q7-c24-ex-24-c-central-tendency-concise-maths-solutions-icse-class-10-1200x708.png)
From graph, C = 28.
Hence, median = 28.
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