Math Assessment Question- anyone who can help?

Question

Mrs Santifort had some pay details that she lost. She had already worked out some summary statistics for them, however, she needs the individual salaries. Develop a set of salaries which qualify the following conditions:

a. There are nine salaries

b. The mode is $41,000

c. The median is $40,000

d. The interquartile range is $10,000

e. The range of the salaries is $25,000

Also, how can I prove that the set of salaries fits the criteria? eg; graph, table etc.

Answer 1

The salaries in $1000 could be:

25, 30, 31, 35, 40, 41, 41, 41, 50.

Call the nine salaries;

a

b

c

d

e=40

f

g

h

i

{In $1,000}

e=40; median

i=a+25; range

g=c+10; interquartile range

g=41; mode

c=31; from g

f or h = 41 or both; mode.

We know the values of c, e and g.

Let both f=h=41 for the mode.

Make i = 50. Then a = 25; range.

Fill in b=30 and d=35.

The salaries in $1000 could be:

25, 30, 31, 35, 40, 41, 41, 41, 50.

Many solutions could fit the criteira.

Only e=40, g=41 and c=31 are fixed.

The others can move around a bit.

If the mean had been specified, the question would be even more challenging.