Answered

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How will adding the value 8 affect the mean and median of the data set 4, 6, 8, 10, 12?


A.
The mean and median will increase by the same amount.


B.
The median will increase more than the mean.


C.
The median will stay the same, but the mean will increase.


D.
The mean and median will both stay the same.

Sagot :

iGreen
4, 6, 8, 10, 12

Mean without 8:

Mean is adding all the numbers and dividing by how many numbers there are.

4 + 6 + 8 + 10 + 12 = 40

40 / 5 = 8

So the mean is 8.

Mean with 8:

4, 6, 8, 8, 10, 12

4 + 6 + 8 + 8 + 10 + 12 = 48

48 / 6 = 8

So the mean is 8.

Median without 8:

4, 6, 8, 10, 12

Median is the middle number. In this case it's 8.

Median with 8:

4, 6, 8, 8, 10, 12

Median is the middle number, there are two 8's in the middle, so the median is 8.

Therefore the mean and the median both stay the same.

Answer:

Option: D is the correct answer.

Both mean and median stay the same.

Step-by-step explanation:

  • We are given a data set as:

4, 6, 8, 10, 12

Clearly from the data set we could see that the median of the set is:

Median=8

( Since we know that the median of the set is the central tendency of a data and always exist in the middle of the data set)

Also, we have 5 data points hence, the mean is calculated as:

[tex]Mean=\dfrac{4+6+8+10+12}{5}\\\\\\Mean=\dfrac{40}{5}\\\\Mean=8[/tex]

Hence, we have:

Mean=8

and Median=8

  • Now when we add another point 8 to the set we have the set in increasing order as:

4,6,8,8,10,12

Hence, now the median lies between 8 and 8.

Hence, we get Median=8

( Since, (8+8)/2=16/2=8)

Also, Mean is calculated as:

[tex]Mean=\dfrac{4+6+8+8+10+12}{6}\\\\Mean=\dfrac{48}{6}\\\\Mean=8[/tex]

Hence, we have:

Mean=8

and Median=8

So, the statement that can be inferred form the addition of a new data point is:

D.

The mean and median will both stay the same.

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