Subject

    Quantitative Aptitude

    Topic

    Average

    An analysis of the monthly incentives received by 5 salesmen: The mean and median of the incentives is 7,Theonlymodeamongtheobservationsis7, The only mode among the observations is 12, Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month?

    ক)
    $4,000
    খ)
    $13,000
    গ)
    $9,000
    ঘ)
    $ 11,000

    Explanation

    The arithmetic mean of 5 observations is 7000.Therefore,thesumofthese5observationsis5∗7000=7000. Therefore, the sum of these 5 observations is 5 * 7000 = 35,000. The median is 7000.Letussaytheirincentivesinascendingorderarea,b,c,dande.So,c=7000anda+b+c+d+e=7000. Let us say their incentives in ascending order are a, b, c, d and e. So, c = 7000 and a + b + c + d + e = 35,000 The only mode is 12,000.So,themaximumnumberofobservationsamongthe5willbein12,000. So, the maximum number of observations among the 5 will be in 12,000. The only possibility is that both d and e got an incentive of 12,000each.So,c+d+e=7000+12000+12000=12,000 each. So, c + d + e = 7000 + 12000 + 12000 = 31,000 Therefore, a + b = 35,000 - 31,000 = 4000. a and b have to be two different values as the only mode is 12,000.So,ahastobe12,000. So, a has to be 1000 and b has to be 3000.Thedifferencebetweenthehighestandthelowestistherefore12,000−1000=3000. The difference between the highest and the lowest is therefore 12,000 - 1000 = 11,000

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