The following table shows the income (in ₹ lakh) and profit percentage of a…
2023
The following table shows the income (in ₹ lakh) and profit percentage of a company over six years from 2017 to 2022.
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 over the six years from 2017 to 2022 was:
Answer: A. ₹ 155 lakh — CONCEPTTo find a median, first arrange all observations in ascending order. For an even number n of observations, the median is the arithmetic mean of the…
- A.
₹ 155 lakh
- B.
₹ 150 lakh
- C.
₹ 160 lakh
- D.
₹ 153.33 lakh
Show answer & explanation
Correct answer: A
CONCEPT
To find a median, first arrange all observations in ascending order.
For an even number n of observations, the median is the arithmetic mean of the observations at positions n/2 and (n/2) + 1.
APPLICATION
Arrange the six income values in ascending order: ₹120, ₹130, ₹150, ₹160, ₹170, and ₹190 lakh.
Here n = 6, so the two central positions are the 3rd and 4th; their values are ₹150 lakh and ₹160 lakh.
Median income = (₹150 lakh + ₹160 lakh) / 2 = ₹310 lakh / 2 = ₹155 lakh.
CROSS-CHECK
There are three income values below ₹155 lakh and three above it, confirming the midpoint of the two central observations.
Therefore, the median income is ₹155 lakh.