17 a set of nine data points is shown below. 8, 11, 12, 10, 9, 7, 5, 3, 9 which statement is true if a tenth…

17 a set of nine data points is shown below. 8, 11, 12, 10, 9, 7, 5, 3, 9 which statement is true if a tenth data point of 45 is added to the data set? a the mean and median will both increase. b the mean will increase and the median will decrease. c the mean will increase and the median will remain the same. d the mean and median will both decrease.

17 a set of nine data points is shown below. 8, 11, 12, 10, 9, 7, 5, 3, 9 which statement is true if a tenth data point of 45 is added to the data set? a the mean and median will both increase. b the mean will increase and the median will decrease. c the mean will increase and the median will remain the same. d the mean and median will both decrease.

Answer

Explanation:

Step1: Calculate the original mean

The sum of the original 9 - data points (8 + 11+12 + 10+9+7+5+3+9=74). The original mean is (\frac{74}{9}\approx8.22).

Step2: Calculate the new mean

When we add a tenth data - point of 45, the new sum is (74 + 45=119). The new mean is (\frac{119}{10}=11.9). So the mean increases.

Step3: Arrange the original data in ascending order

The original data in ascending order is (3,5,7,8,9,9,10,11,12). Since (n = 9) (odd), the median is the (\left(\frac{9 + 1}{2}\right))-th value, which is the 5 - th value, and the median is 9.

Step4: Arrange the new data in ascending order

The new data in ascending order is (3,5,7,8,9,9,10,11,12,45). Since (n = 10) (even), the median is the average of the (\frac{10}{2})-th and (\left(\frac{10}{2}+1\right))-th values. The 5 - th value is 9 and the 6 - th value is 9, so the median is (\frac{9 + 9}{2}=9). The median remains the same.

Answer:

C. The mean will increase and the median will remain the same.