Question

# Calculate mode from the following data: Wages (βΉ) Number of Workers Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 15 35 60 84 96 127 198 250

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Solution

## To calculate the value of mode, we first convert the given less than cumulative frequency distribution into a simple frequency distribution as follows. Wages No. of Wages (f) 0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 15 35 − 15 = 20 60 − 35 = 25 84 − 60 = 24 97 − 84 = 12 127 − 96 = 31(f0) 198 − 127 = 71 (f1) 250 − 198 = 52 (f2) By inspection, we can say that the modal class is 60 – 70 as it has the highest frequency of 71. $\mathrm{Mode}\left(Z\right)={l}_{1}+\frac{{f}_{1}-{f}_{0}}{2{f}_{1}-{f}_{0}-{f}_{2}}×i\phantom{\rule{0ex}{0ex}}\mathrm{or},Z=60+\frac{71-31}{2\left(71\right)-31-52}×10\phantom{\rule{0ex}{0ex}}\mathrm{or},Z=60+\frac{40}{142-83}×10\phantom{\rule{0ex}{0ex}}\mathrm{or},Z=60+\frac{400}{59}\phantom{\rule{0ex}{0ex}}\mathrm{or},Z=60+6.78=66.78\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{Mode}\mathrm{is}66.78$

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