Question Details

The following table shows the Income (in lakh) and percentage (%) profit of a company over the six years from 2017 to 2022. Based on the data in the table, answer the questions that follow.

Year-wise Income and Profit of a Company

Year  Income (in ₹ lakh) Profit (%)
 
2017 120 7.5
2018 160 15
2019 130 22.5
2020 170 17.5
2021 190 20
2022 150 27.5

The median income of the company in the six years from 2017 to 2022 was

Options

A

155 lakh

B

150 lakh

C

160 lakh

D

153.33 lakh

Show Answer

Correct Answer :

Option A

155 lakh

Solution :

The correct option is 155 lakh.

To find the median income of the company over the six years from 2017 to 2022, we first extract the income values for each year from the given table:
- 2017: 120 lakh
- 2018: 160 lakh
- 2019: 130 lakh
- 2020: 170 lakh
- 2021: 190 lakh
- 2022: 150 lakh

Next, we arrange these income values in ascending order:
120, 130, 150, 160, 170, 190

The number of observations (years) is n=6, which is an even number.
For an even number of observations, the median is calculated as the average of the two middle terms, which are the n2th and the n2+1th terms.

Here, the middle terms are the 3rd and 4th values in our sorted list:
- 3rd term = 150 lakh
- 4th term = 160 lakh

Now, we calculate the average of these two middle values to find the median:
Median Income = 150 + 160 2
Median Income = 310 2 = 155 lakh

Therefore, the median income of the company was 155 lakh.

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