consider the data set 11,12,13,14,15,16,17,18,19. complete parts (a) through (c) below.\na. obtain the mean…

consider the data set 11,12,13,14,15,16,17,18,19. complete parts (a) through (c) below.\na. obtain the mean and median of the data.\nthe mean is 15.\n(type an integer or a decimal. do not round.)\nthe median is 15.\n(type an integer or a decimal. do not round.)\nb. replace the 19 in the data set by 109 and again compute the mean and median. decide which measure of center works better here, and explain your answer.\nthe mean is \n(type an integer or a decimal. do not round.)

consider the data set 11,12,13,14,15,16,17,18,19. complete parts (a) through (c) below.\na. obtain the mean and median of the data.\nthe mean is 15.\n(type an integer or a decimal. do not round.)\nthe median is 15.\n(type an integer or a decimal. do not round.)\nb. replace the 19 in the data set by 109 and again compute the mean and median. decide which measure of center works better here, and explain your answer.\nthe mean is \n(type an integer or a decimal. do not round.)

Answer

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are data - points and $n$ is the number of data - points. After replacing 19 with 109, the data set is 11, 12, 13, 14, 15, 16, 17, 18, 109 and $n = 9$.

Step2: Calculate the sum of data - points

$\sum_{i=1}^{9}x_{i}=11 + 12+13 + 14+15+16+17+18+109=224$.

Step3: Calculate the mean

$\bar{x}=\frac{224}{9}\approx24.888\cdots=\frac{224}{9}$.

Step4: Recall median formula

For a set of $n = 9$ (odd number of) data - points arranged in ascending order, the median is the $\left(\frac{n + 1}{2}\right)$-th value. The ordered data set is 11, 12, 13, 14, 15, 16, 17, 18, 109. $\frac{n + 1}{2}=\frac{9+1}{2}=5$. So the median is 15.

Step5: Analyze which measure is better

The median is a better measure of the center here. The mean is affected by the outlier (109), pulling it towards the outlier value. The median, on the other hand, is the middle - value and is not affected by extreme values.

Answer:

The mean is $\frac{224}{9}$. The median is 15. The median is a better measure of center because the mean is affected by the outlier 109, while the median is not.