Question

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

Answer 1

Answer:

Step-by-step explanation:

Given :-

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.

To Find :-

The greatest integer in the new group.

Solution :-

⇒ Mean = (3 + 4 + 5 + 5 + 8) /5 = 5

⇒ Median = 5

⇒ Mode = 5

Four integers are added to a group increases by 1 each,

⇒ Mode = 6

Let fourth integer be x .

Group of integers = 3, 4, 5, 5, 6, 6, 6, 8 and x.

⇒ (3 + 4 + 5 + 5 + 6 + 6 + 6 + 8 + x)/9 = 6

⇒ (43 + x)/9 = 6

⇒ 43 + x = 54

⇒ x = 54 - 43

⇒ x = 11.

​Hence, the greatest integer in the new group of integers  is 11.

Answer 2

$\huge{\mathfrak{ \overbrace{ \underbrace{ \pink{ \fbox{ \green{ \blue{A} \pink{n} \red{s} \green{w} \purple{e} \blue{r}}}}}}}}</p><p>$

$\sf{ \underline{ \underline{ \red{Given}}}}: -$

Four integers are added to a group of integers 3, 4, 5, 5 and 8 & the mean, median, mode of the data increases by 1 each.

$\sf{ \underline{ \underline{ \orange{To \: find}}}}: -$

The greatest integer in the new group of integers.

$\sf{ \underline{ \underline{ \blue{Solution}}}}: - \\ ⇒ \bf{Mean = \frac{(3 + 4 + 5 + 5 + 8)}{5} } \\ ⇒ \bf{Mean = \frac{25}{5} } \\ ⇒ \bf{Mean = 5} \\ \\ ⇒ \bf{Median = 5} \\ \\ ⇒ \bf{Mode = 5} \\ \\ \bf{Four \: integers \: are \: added \: to \: a \: group \: } \\ \bf{increases \: by \: 1 \: each.} \\ \\ ⇒ \bf{Mode = Median = Mean = 6} \\ \\ \bf{Let ,\: fourth \: integer \: be \: x.} \\ \\ \bf{So, \: group \: of \: integers = 3,4,5,5,6,6,6,8 \:and \: x.} \\ \\ ⇒ \bf{ \frac{(3 + 4 + 5 + 5 + 6 + 6 + 6 + 8 + x)}{9} = 6 } \\ ⇒ \bf{ \frac{(43 + x)}{9} = 6 } \\ ⇒ \bf{43 + x = 54} \\ ⇒ \bf{x = 54 - 43} \\ ⇒ \bf{x = 11}$

Therefore, the greatest integer in the new group of integers is 11.