Question

A selection of staff wages is collected and shown below.

£254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £239 £700
What is the mode of staff wages? £ 254 and £ 180
What is the median of the staff wages? £ 248.5
What is the mean of the staff wages? £ 276.625
Select the most appropriate average, mean, median or mode.

Answer 1

Modes of staff wages are £180 and £254.

Median of staff wages is £248.5

Mean of staff wages is £276.625

Explanation:

Given list of staff wages is.....

£254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £239 £700

Rearranging the data according to ascending order.....

£90 £116 £165 £180 £180 £221 £239 £243 £254 £254 £276 £310 £312 £350 £536 £700

The mode is the number repeated most often. This list has two values that are repeated two times, which are £180 and £254.

So, the modes are: £180 and £254

Median is the middle value in the list. As there are total 16 numbers, so the middle value will be the average of 8th and 9th numbers, which are £243 and £254 respectively.

So, the median will be:
`((243+254)/(2))=(497)/(2)=248.5`

The mean is the simple average of all numbers in the list. There are total 16 numbers.

So, the mean will be:

`(90+116+165+180+180+221+239+243+254+254+276+310+312+350+536+700)/(16)\\ \\ =(4426)/(16)=276.625`