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The correct option is (E) 85.
The correct average number of stamps in the 10 collections is 85.
What is average number?
It's the arithmetic mean, which is produced by adding a set of numbers and and afterwards dividing by the number of numbers in the set.
Now, according to the question;
Given that the number of the total collections = 10,
The average number of stamps within each of the ten collections is 88.
However, two numbers are incorrectly entered.
55 is entered as 75, and 78 as 88.
Let us now assume that the total number of stamps as in leftover 8 collections, excluding the above 2, is x.
Because the initial average number of stamps in the ten collections was 88,
(Total number of stamps in 10 collections)/(number of collections) = 88.
(x + 75 + 88)/10 = 88
(x + 75 + 88) = 880
x = 880 - 163
x = 717
Now, in order to determine the correct average number of stamps with in ten collections,
Average number of stamps throughout 10 collections =
(Total number of stamps in 10 collections)/(number of collections)
= (x + 55 + 78)/10
= 850/10
= 85
Therefore, Average number of stamps throughout 10 collections is 85.
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The complete question is -
A stamp collecting club calculated that the average (arithmetic mean) number of stamps in its members 10 collections was 88. However, it was discovered that 2 numbers in the calculations were entered incorrectly. The number 55 was entered as 75 and the number 78 as 88. What is the correct average number of stamps in the 10 collections?
(A) 91
(B) 89
(C) 87
(D) 86
(E) 85
