Respuesta :
You can use the fact that median is affected only if the middle value(s) are changed if number of values are same.
- The mean salary will become $4000 less than previous mean of salaries.
- The median will stay same as before.
How are mean and median affected if a value is changed to some other value?
The median is the middle value of the sorted(ordered in ascending or descending way)data values. If value changed is not the middle value (if number of observations are odd) or is not changing the average of two mid values (if number of observations are even), then the median won't change as it does't care about the value of the data unless its about the mid value of the sorted data or average of mid values.
The mean is affected by the data.
The mean of n values is calculated as:
[tex]\overline{x} = \dfrac{x_1 + x_2 + ... + x_i + ... + x_n}{n}[/tex]
Suppose that x_i changed to y
Then we have then new mean as
[tex]\begin{aligned}\overline{x}_{new} &= \dfrac{x_1 + x_2 + ... + (x_i -x_i + y)+ ... + x_n}{n}\\&= \dfrac{x_1 + x_2 + ... + x_i+ ... + x_n}{n} + \dfrac{-x_i + y}{n}\\&= \overline{x} + \dfrac{y-x_i}{n}\\\end{aligned}[/tex]
For the given data, one value was changed from $40,000 to $20,000, thus, as $40,000 was lowest value of the data, thus median stays same as before,.
And for new mean, we have:
[tex]\overline{x}_{new} = \overline{x} + \dfrac{y-x_i}{n} = \overline{x} + \dfrac{-20000}{5}\\\\\overline{x}_{new} = \overline{x} -4000[/tex]
Thus, new mean salary will be $4000 less than the previous mean salary.
Learn more about mean versus median here:
https://brainly.com/question/14315366
