Question

Four integers are added to a group integers 3, 4, 5, 5, 8 and the mean, median, and mode of the data increases by 1 each . what is the greatest integer in the new group of integers?

Answer 1

Solution:-
The given integers are 3, 4, 5, 5 and 8.
Mean = (3 + 4 + 5 + 5 + 8)/5
= 25/5
Mean = 5
Median = 5
and Mode = 5 (Mode is the most frequently occurring value)
After adding 4 integers, mode is increased by 1,
Therefore, the new mode is 6.
Since, the mode is most frequently occurring value, there 6 must be added at least three times.
So, the new set of integers will be 3, 4, 5, 5, 6, 6, 6, 8 and x.
Let the 4th integers be 'x'.
And the new mean is 6.
6 = (3 + 4 + 5 + 5 + 6 + 6 + 6 + 8 + x)/9
(43 + x)/9 = 6
43 + x = 54
x = 54 - 43
x = 11
So, greatest of the four integers that are added is 11.
Answer.