The following table gives the installation time (in minutes) for hardware on 50 different computers.

Installation Time 0-10 10-20 20-30 30-40 40-50 Total
Number of computers 4 10 10 50

If the average installation time is 30.2 minutes, find missing frequencies.

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Let x and y be the missing frequencies. Now, Let’s construct the table:

Given, x̄ = 30.2

class(x) No.(f) m fm
0-10 4 5 20
10-20 x 15 15x
20-30 10 25 250
30-40 y 35 35y
40-50 10 45 450
N = 50 = 24 + x + y Σfm = 720 + 5x + 35y

Now, from table

24 + x + y = 50

x + y = 26  ——— (i)

Also,

15x  + 35y + 720 = 30.2 x 50

15x + 35y = 790 ———–(ii)

Solving equation i) and ii)

\(\frac{\begin{matrix} 15x \enspace + \enspace 15y \enspace = \enspace 390\\ 15x \enspace + \enspace 35y \enspace
= \enspace 790 \end{matrix}}{ – 20y\enspace = \enspace – 400 }\)

y = 20

When, y = 20

x + 20 = 26

x = 6

The missing frequencies are 20 and 6

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