The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data. Average Speed of Vehicles (Km/hr) - Algebra

Sum

The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.

 Average Speed of Vehicles (Km/hr) 60 - 64 64 - 69 70 - 74 75 - 79 79 - 84 84 - 89 No. of vehicles 10 34 55 85 10 6

Solution

 Class (Average speed of vehicles (km/hr)) Continuousclasses Frequency(Number of workers) Cumulative frequency less than theupper limit 60 - 64 59.5 - 64.5 10 10 64 - 69 64.5 - 69.5 34 44 70 - 74 69.5 - 74.5 55 99 → cf 75 - 79 74.5 - 79.5 85 → f 184 79 - 84 79.5 - 84.5 10 194 84 - 89 84.5 - 89.5 6 200 Total N = 200

Here, total frequency = ∑fi = N = 200

∴ "N"/2 = 200/2 = 100

Cumulative frequency, which is just greater than (or equal) to 100, is 184.

∴ The median class is 74.5 – 79.5.

Now, L = 74.5, f = 85, cf = 99, h = 5

Now,

∴ Median = "L" + (("N"/2 - "cf")/"f") × "h"

= 74.5 + ((100 - 99)/85) xx 5

= 74.5 + 1/85 xx 5

= 74.5 + 1/17

= 74.5 + 0.0588

= 74.558 ≈ 75

∴ The median of the given data is 75 km/hr.

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Chapter 6: Statistics - Practice Set 6.2 [Page 145]

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Balbharati Maths 1 Algebra 10th Standard SSC Maharashtra State Board
Chapter 6 Statistics
Practice Set 6.2 | Q 3 | Page 145

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