Read the information given below carefully and answer the question that follows:
(A) If the mean of 5 numbers is 15 and then if 27 is included to the numbers, then the mean of the 6 numbers shall be 17
(B) The mean of marks of 300 students is 60, the mean of the top 100 students' marks is 80 and the mean of the last 100 students is 50, then the mean of the marks of the rest of the 100 students of the group is 60.
(C) The mean and median of 5 observations is 9 and 8 respectively, if 1 is subtracted from each observation, then the new mean and median shall be 8 and 7 respectively
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (C) Only
The mean is the sum of the observations divided by their number, so a sum can always be recovered as mean × number. The median is the middle value when the observations are in order.
(A) If the mean of 5 numbers is 15 and then if 27 is included to the numbers, then the mean of the 6 numbers shall be 17 Correct.
Sum of the 5 numbers \(=5\times15=75\)
Sum after adding 27 \(=75+27=102\)
New mean \(=102\div6=17\)
(B) The mean of marks of 300 students is 60, the mean of the top 100 students' marks is 80 and the mean of the last 100 students is 50, then the mean of the marks of the rest of the 100 students of the group is 60. Incorrect. The middle 100 students have a mean of 50, not 60:
Total marks of all 300 \(=300\times60=18000\)
Top 100 \(=100\times80=8000\); last 100 \(=100\times50=5000\)
Middle 100 \(=18000-8000-5000=5000\), so their mean \(=5000\div100=50\)
(C) The mean and median of 5 observations is 9 and 8 respectively, if 1 is subtracted from each observation, then the new mean and median shall be 8 and 7 respectively Correct. Subtracting the same number from every observation lowers the sum by 5 × 1, so the mean falls by 1, to 8. The order of the observations does not change, so the middle one also falls by 1, and the median becomes 7.