Subjects statistics

Salary Statistics B2Cbf4

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1. **Problem:** Compute the mean, median, and mode of the monthly salaries: 3, 3, 3, 4, 5, 6, 7, 10, 12, 15, 20, 30, 50, 70, 100. 2. **Mean formula:** $$\text{Mean} = \frac{\text{Sum of all salaries}}{\text{Number of salaries}}$$ 3. **Calculate the sum:** $$3+3+3+4+5+6+7+10+12+15+20+30+50+70+100 = 338$$ 4. **Calculate the mean:** $$\text{Mean} = \frac{338}{15} = 22.53$$ (rounded to two decimals) 5. **Median:** The middle value when data is ordered. Since there are 15 values (odd), median is the 8th value. 6. **Ordered data:** 3, 3, 3, 4, 5, 6, 7, 10, 12, 15, 20, 30, 50, 70, 100 7. **Median value:** 10 (the 8th value) 8. **Mode:** The most frequent value(s). Here, 3 appears 3 times, more than any other number. 9. **Mode:** 3 --- 10. **Best measure to represent typical salary:** Median, because it is not affected by extreme values and represents the middle salary. 11. **Advertising average salary:** Mean, because it is higher due to large salaries and makes the average appear more attractive. 12. **Effect of replacing highest salary 100 with 150:** 13. New sum: $$338 - 100 + 150 = 388$$ 14. New mean: $$\frac{388}{15} = 25.87$$ 15. Median remains the 8th value in ordered data: 3, 3, 3, 4, 5, 6, 7, 10, 12, 15, 20, 30, 50, 70, 150 Median = 10 (unchanged) 16. **Summary:** Mean increases from 22.53 to 25.87 due to the outlier increase, median stays at 10.