Multiple choice

The mean of $21$ observations (all different) is $40 .$ If each observations greater than the median are increased by $21 ,$ then mean of observations will become

  1. $50$
  2. $50.5$
  3. $30$
  4. $45$
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A Correct answer
Explanation

Let the observations be x1, x2, ..., x21. Mean = sum/21 = 40, so sum = 840. If observations greater than the median are increased by 21, the sum increases by (number of observations > median) * 21. Since there are 21 observations, 10 are greater than the median. Increase = 10 * 21 = 210. New sum = 840 + 210 = 1050. New mean = 1050 / 21 = 50.

AI explanation

Since there are 21 observations, the median is the 11th value, leaving 10 observations above the median. When these 10 values are each increased by 21, the total increase in the overall sum of the observations is 10 * 21 = 210. Dividing this total increase of 210 by the 21 observations shows the mean increases by 10. Adding this increase of 10 to the original mean of 40 results in a new mean of 50.

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