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We have analyzed the monthly salaries received by $5$ employees : The mean and median of the salaries is $\$7000$. The only mode among the observations is $\$12,000$. Salaries paid to each employee were in full thousands. What is the difference between the highest and the lowest salary received by the $5$ employees in the month ?

  1. $\$4000$
  2. $\$13,000$
  3. $\$5000$
  4. $\$11,000$
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Option D. $11,000

Given, Mean = \$7000  i.e. Sum of all the salaries of 5 employees = 5 * \$7000 = \$35000

Median = \$7000 i.e.  __ __  \$7000 __ __ 

only Mode = \$12000 i.e. __ __ \$7000 \$12000 \$12000

then sum of 1st and 2nd = 35,000 - 31,000 = \$4000

As there is only one mode, the salaries received by 1st and 2nd have to be different.

So, 1st received \$1000 and 2nd received \$3000. [i.e. \$1000 \$3000 \$7000 \$12000 \$1200 ]

difference between the highest and the lowest salary = 12000 – 1000 = \$11000

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