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# The table below shows the salaries of 280 persons.

Calculate the median and mode of the data.

Answer :

First, we construct a cumulative frequency table

∴ N/2 = 280/2 = 140

(i) Here, median class is 10 - 15, because 140 lies in it.

Lower limit(l) = 10,

Frequency(f) = 133

Cumulative frequency (f_{c}) = 49 and class width (h) = 5

= 10 + 3.421

= Rs.13.421 (in thousand)

= 13.421× 1000

= Rs.13421

(ii) Here, the highest frequency is 133, which lies in the interval 10 - 15, called modal class.

Lower limit(l) = 10, class width(h) = 5,

f_{m} = 133,

f_{1} = 49 and

f_{2} = 63

= 10 + 2.727

= Rs.12.727 (in thousand)

= 12.727 × 1000 = Rs.12727

Hence, the median and modal salary are Rs.13421 and Rs12727, respectively.

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