Question

A library give every employee a $500 bonus. What effect, if any does it have on(a) mean (b) median (c) mode (d) Standard division

Answer 1

The mean is the

sum of salaries/number of employees

Assuming the salaries of 5 employees were

1000, 2000, 3000, 4000, 4000

Mean = (1000 + 2000 + 3000 + 4000, 4000)/5 = 2800

If we add a bonus of $500 to each, we have

1500, 2500, 3500, 4500, 4500

Mean = (1500 + 2500 + 3500 + 4500 + 4500)/5 = 3300

Thus, the mean increases

The median is the middle value

The middle value was 3000, the new median is 3500

The median increases

The mode is the value with the highest frequency. The former mode is 4000. The new mode is 4500

the mode increases

The standard deviation is how far the values are from the mean

Standard deviation = Square root of the square of (each value - mean)/ number of values. Thus, we have