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Income Distribution

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Income Distribution


1. **Problem Statement:** We have monthly incomes (in thousands of BDT) of 9 employees: 22, 25, 27, 24, 30, 21, 100, 23, 26. We need to find the mean and median income and determine which measure better represents the typical income. 2. **Calculate the Mean:** - Sum all incomes: $$22 + 25 + 27 + 24 + 30 + 21 + 100 + 23 + 26 = 298$$ - Count the number of employees: $$9$$ - Mean income $$= \frac{298}{9} \approx 33.11$$ thousand BDT. 3. **Calculate the Median:** - Sort incomes in ascending order: $$21, 22, 23, 24, 25, 26, 27, 30, 100$$ - Median is the middle value for odd number of data points, i.e., the 5th value. - Median income $$= 25$$ thousand BDT. 4. **Compare Mean and Median:** - The mean $$\approx 33.11$$ thousand BDT is higher than the median $$25$$ thousand BDT due to the extremely high income of 100 thousand BDT, which is an outlier. - The median better represents the typical income here because it is not affected by the outlier, while the mean is pulled higher. **Final Answer:** - Mean income = $$33.11$$ thousand BDT. - Median income = $$25$$ thousand BDT. - The median better represents the typical income because it is resistant to the outlier effect of the very high income.