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The Following Table Shows the Classification of Number of Vehicles and Their Speeds on Mumbai-pune Express Way. Find the Median of the Data. - Algebra

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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
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Solution

Class
(Number of working hours)
Continuous
classes
Frequency
(Number of workers)
 
Cumulaive frequency 
less than the
upper 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 = \[L + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h\]\

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

= 74.5 + 0.059

= 74.559 ≈ 75

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

Concept: Tabulation of Data
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APPEARS IN

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