Analysis on monthly incentive of 5 salesman shows the mean & median of the incentives is $7000. The mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest?

1 Answer
EZ as pi
Aug 29, 2016

#$12,000 - $1,000 = $11,000#

Explanation:

Summarise the facts:

There are 5 salesmen and the mean of the incentives is 7,000
The median is 7,000 - in the middle
The mode is #12,000 rarr "at least 2 values of "12,000#

The first value we can calculate is the TOTAL amount (the sum of all the incentives)

#"TOTAL"/5 = 7,000#

# rArr TOTAL= 5xx7.000 = 35,000#

The middle value is 7000: So now, in order we have:

# ............... ; .................; 7,000; .....................; ........................#

#12,000# must occur exactly twice to be the mode..

# ............... ; .................; 7,000; 12,000; 12,000.#

The remaining two values must add up to....

#35,000 - 7,000 - 2xx 12,000 =4,000#

They have to be full thousands: The amounts must be different otherwise there will be two modes, (So, it is not #2,000+2,000#)

#1,000 + 3,000 = 4,000#

The five amounts are:

#1,000 ; 3,000 ; 7,000 ; 12,000 ; 12,000#

Highest - lowest = #12,000-1,000 = 11,000#

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