Question

four integers are added to a group of integers 3,4,5,5 and 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

Mean=(3+4+5+5+8)÷5=25÷5=5
Median=5
Mode=5(as 5 has frequency 2)
four integers are added to a group of integers
data increases by 1 each so
Mode=6
In group of integers 6 must be 3 times,So
Let fourth integer=x
Group of integers=3,4,5,5,6,6,6,8 and x
So new mean is 6
(3+4+5+5+6+6+6+8+x)÷9=6
(43+x)÷9=6
43+x=54
x=54-43
x=11
Answer-11 is the greatest integer in the new group of integers.

Answer 2

Answer:

Step-by-step explanation:

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

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