Answer:
a) $42,580
b) $43,900
Explanation:
Recall, "mode" refers to the value which occurs most frequently.
In this case, the question says that there are 2 modes,
this means $34,000 and $50,500 both share the spot for the most frequently appearing salary.
because there are only 5 employees (and hence 5 salaries), the only possible way that there are two modes is if there are two of each mode, leaving only the last salary unknown.
i.e if we list the 5 salaries (in no particular order)
$34,000 $34,000 $50,500 $50,500 $ x
where x is the 5th unknown salary.
Given that the mean is $42,100
Then (34,000 + 34,000 + 50,500 + 50,500 + x) / 5 = 42,100
solving for x gives x = $41,500
Now we know all the values, we can rearrange them in increasing value:
$34,000 $34,000 $41,500 $50,500 $50,500
from this, we can see that the median salary is $41,500
Given that the median salary gets a $2400 raise,
the new median salary = $41,500 + $2400 = $43,900 (Ans for part b)
new mean salary,
= ($34,000 + $34,000 + $43,900 + $50,500 + $50,500 ) / 5
= $42,580 (answer for part a)