Question

② The following table gives the distribution
of weekly wages of 600 workers of a factory;
Weekly wages Frequency Obtain the
limits of weekly wages of central 50 % of the workers
Below 375
69
375 - 450
167
wages of central
50 percent of
450 – 525
207
the workers
525- 600
65
58
600 675
675 - 750
750- 825
24
10​

Answer 1

Answer:

The limits of weekly wages for the central 50% of workers are approximately 480.4 to 635.65.

Explanation:

To find the limits of weekly wages of the central 50% of workers, we need to first arrange the given frequency distribution in ascending order of wages.

Weekly Wages Frequency

Below 375 69

375 - 450 167

450 – 525 207

525- 600 65

600 - 675 58

675 - 750 24

750 - 825 10

Next, we need to calculate the cumulative frequencies and cumulative relative frequencies:

Weekly Wages Frequency Cumulative Cumulative Relative Frequency

Frequency

Below 375 69 69 0.115

375 - 450 167 236 0.393

450 – 525 207 443 0.738

525- 600 65 508 0.847

600 - 675 58 566 0.943

675 - 750 24 590 0.983

750 - 825 10 600 1.000

The cumulative relative frequency column shows that the central 50% of workers correspond to the cumulative relative frequency between 0.25 and 0.75, which means that we need to find the wages limits that correspond to the cumulative frequencies of 0.25 and 0.75.

To find the lower limit of wages for the central 50% of workers, we need to find the wage value corresponding to a cumulative frequency of 0.25. From the cumulative frequency column, we see that the cumulative frequency just below 0.25 is 0.115, corresponding to wages below 375. The next cumulative frequency is 0.393, corresponding to wages in the range of 375-450. To get a cumulative frequency of exactly 0.25, we need to interpolate between these two wage ranges:

0.25 = (x - 69)/(167) => x = 105.4

Therefore, the lower limit of weekly wages for the central 50% of workers is approximately 105.4 + 375 = 480.4.

Similarly, to find the upper limit of wages for the central 50% of workers, we need to find the wage value corresponding to a cumulative frequency of 0.75. From the cumulative frequency column, we see that the cumulative frequency just below 0.75 is 0.738, corresponding to wages in the range of 450-525. The next cumulative frequency is 0.847, corresponding to wages in the range of 525-600. To get a cumulative frequency of exactly 0.75, we need to interpolate between these two wage ranges:

0.75 = (x - 443)/(207) => x = 601.65

Therefore, the upper limit of weekly wages for the central 50% of workers is approximately 600 + (601.65 - 566) = 635.65.

Therefore, the limits of weekly wages for the central 50% of workers are approximately 480.4 to 635.65.

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