Calculating Median Income of the Company (2017-2022)

The question asks for the median income of the company over the six years from 2017 to 2022. The median is the middle value in a dataset when the data is arranged in order. If there is an even number of data points, the median is the average of the two middle values.

Understanding the Data Table

The provided table gives the Income (in Rs. lakh) and percentage (%) profit for the company for each year from 2017 to 2022. For this question, we only need the 'Income' data.

Steps to Calculate the Median Income

Here are the steps to find the median income:

1. List the income values from the table.
2. Arrange the income values in ascending order (from smallest to largest).
3. Identify the middle value(s). Since there are 6 years (an even number of data points), the median will be the average of the two middle values.
4. Calculate the average of the two middle values.

Applying the Steps

Let's apply these steps to the given income data:

• The income values are: 120, 160, 130, 170, 190, 150.
• Arranging these values in ascending order gives: 120, 130, 150, 160, 170, 190.
• There are 6 values. The middle two values are the 3rd and 4th values in the sorted list. These are 150 and 160.
• The median is the average of 150 and 160.

Median Calculation:

\( \text{Median} = \frac{\text{Value at position } \frac{n}{2} + \text{Value at position } \frac{n}{2} + 1}{2} \)

Where \( n \) is the number of data points (which is 6 here).

\( \text{Median} = \frac{\text{3rd value} + \text{4th value}}{2} \)

\( \text{Median} = \frac{150 + 160}{2} \)

\( \text{Median} = \frac{310}{2} \)

\( \text{Median} = 155 \)

So, the median income of the company over the six years is Rs. 155 lakh.

Final Answer

Based on the calculation, the median income is Rs. 155 lakh.

Revision Table: Data Analysis Concepts

Additional Information: Understanding Median and Data Order

The median is a measure of central tendency that is particularly useful when a dataset might have outliers (extremely high or low values) because it is not affected by outliers as much as the mean is. Ordering the data is a crucial first step in finding the median.

For an even number of data points, say \( n \), the median is found between the \( \frac{n}{2} \)th and \( (\frac{n}{2} + 1) \)th positions after sorting. For our 6 data points, \( n=6 \), so we look at the \( \frac{6}{2} = 3 \)rd and \( (\frac{6}{2} + 1) = 4 \)th positions.

In this case, the sorted incomes were 120, 130, 150, 160, 170, 190. The 3rd value is 150 and the 4th value is 160. The median is the average of these two: \( \frac{150+160}{2} = 155 \).