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

Four integers are added to a group of integers 3, 4, 5, 5 and 8 and t

1.	Four integers are added to a group of integers 3, 4, 5, 5 and 8 and the mean, median, andmode of the data increases by 1 each. What is the greatest integer in the new group ofintegers?
Answer» Solution:-The given integers are 3, 4, 5, 5 and 8.Mean = (3 + 4 + 5 + 5 + 8)/5= 25/5Mean = 5Median = 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 = 643 + x = 54x = 54 - 43x = 11So, greatest of the four integers that are added is 11.