The Production of Electric Bulbs in Different Factories is Shown in the Following Table. Find the Median of the Productions. - Algebra

Sum

The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.

 No. of bulbs produced (Thousands) 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of factories 12 35 20 15 8 7 8

Solution

 Class (Number of bulbs produced in thousands) Frequency(Number of factories)fi Cumulaive frequencyless than theupper limit 30 - 40 12 12 40 - 50 35 47 50 - 60(Median Class) 20 67 60 - 70 15 82 70 - 80 8 90 80 - 90 7 97 90 - 100 8 105 N = 105

From the above table, we get
L (Lower class limit of the median class) = 50
N (Sum of frequencies) = 105
h (Class interval of the median class) = 10
f (Frequency of the median class) = 20
cf (Cumulative frequency of the class preceding the median class) = 47
Now, Median = $L + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h$
$= 50 + \left( \frac{\frac{105}{2} - 47}{20} \right) \times 10$
= 50 + 2.75
= 52.75 thousand lamps
= 52750 lamps
Hence, the median of the productions is 52750 lamps.

Concept: Tabulation of Data
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Balbharati Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board
Chapter 6 Statistics
Practice Set 6.2 | Q 4 | Page 146