Question 21.
Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?
Question Explanation
The first clue is the minimum value provided:
That is not one of the eleven values that we already have; this must mean that one of the missing values, A or B, must be 2
Since we are given that A is less than B, it must be A, which is equal to 2.
Now, writing down the twelve known numbers,
2, 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29
we are also provided that the median of the data set was 12, which would be possible if the value 12 was shifted from the 6th position to the 7th position.
This must mean that the other missing value would also be in the first 6 values of the data set, lying in the range
Now, narrowing down our focus to the lower hinge, the value is given to be 6.5
The first six values would be 2, 5, 6, 7, 8 and one unknown value
The lower hinge would be 6.5 only if the missing value appears after 7
Narrowing down the possible values of B to be 7, 8, 9, 10, 11, 12
In order to find the average work-experience of all the teachers, we must add up all the values
adding up the known values we get
2+5+6+7+8+12+16+19+21+21+27+29 = 173
Looking at the options, the total sum of all 13 values must be
A: 156
B: 162.5
C: 169
D: 175.5
E: 182
The sum of 13 values can only be 182 of all the given options, which would be the case when B is 9
Therefore, option E is the correct answer.
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