Question

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

Answer 1

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:

$Mean=\dfrac{4+6+8+10+12}{5}\\\\\\Mean=\dfrac{40}{5}\\\\Mean=8$

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:

$Mean=\dfrac{4+6+8+8+10+12}{6}\\\\Mean=\dfrac{48}{6}\\\\Mean=8$

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.

Answer 2

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.