Question

consider the data set 10,11,12,13,14,15,16,17,18. complete parts (a) through (c) below.
a. obtain the mean and median of the data.
the mean is 14.
(type an integer or a decimal. do not round.)
the median is 14.
(type an integer or a decimal. do not round.)
b. replace the 18 in the data set by 108 and again compute the mean and median. decide which measure of center works better here, and explain your answer.
the mean is 24.
(type an integer or a decimal. do not round.)
the median is 14.
(type an integer or a decimal. do not round.)
which center of measure works better here?
a. the median works better here since it is more typical of most of the data.
b. neither measure of center works for this data set. neither measure of center is typical of most of the data.
c. the mean works better here since it is more typical of most of the data.
d. both centers of measure work equally well here. they are both typical of most of the data.

Explanation:

Step1: Recall mean and median formulas

Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, median is middle - value for odd - sized data set or average of two middle - values for even - sized data set.

Step2: Calculate mean for original data set

The original data set is $10,11,12,13,14,15,16,17,18$. $n = 9$, $\sum_{i=1}^{9}x_{i}=10 + 11+12+13+14+15+16+17+18=\frac{(10 + 18)\times9}{2}=126$. Mean $\bar{x}=\frac{126}{9}=14$. Since $n = 9$ (odd), the median is the 5th value, which is 14.

Step3: Calculate mean and median for new data set

Replace 18 with 108. New data set: $10,11,12,13,14,15,16,17,108$. $n = 9$, $\sum_{i = 1}^{9}x_{i}=10+11 + 12+13+14+15+16+17+108=216$. Mean $\bar{x}=\frac{216}{9}=24$. Since $n = 9$ (odd), the median is still the 5th value, which is 14.

Step4: Analyze measure of center

The out - lier 108 greatly affects the mean. The median remains the same as most of the data values are in the range 10 - 17. The median is more typical of most of the data.

Answer:

a. Mean: 14, Median: 14
b. Mean: 24, Median: 14
A. The median works better here since it is more typical of most of the data.