consider the data set 10,11,12,13,14,15,16,17,18. complete parts (a) through (c) below.\na. obtain the mean…

consider the data set 10,11,12,13,14,15,16,17,18. complete parts (a) through (c) below.\na. obtain the mean and median of the data.\nthe mean is 14.\n(type an integer or a decimal. do not round.)\nthe median is 14.\n(type an integer or a decimal. do not round.)\nb. 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.\nthe mean is \n(type an integer or a decimal. do not round.)

consider the data set 10,11,12,13,14,15,16,17,18. complete parts (a) through (c) below.\na. obtain the mean and median of the data.\nthe mean is 14.\n(type an integer or a decimal. do not round.)\nthe median is 14.\n(type an integer or a decimal. do not round.)\nb. 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.\nthe mean is \n(type an integer or a decimal. do not round.)

Answer

Explanation:

Step1: Calculate the sum of new data

The new data - set is 10, 11, 12, 13, 14, 15, 16, 17, 108. The sum of these numbers is (10 + 11+12 + 13+14+15+16+17+108=226).

Step2: Calculate the new mean

The number of data - points (n = 9). The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), so (\bar{x}=\frac{226}{9}\approx25.111).

Step3: Calculate the new median

First, arrange the data in ascending order: 10, 11, 12, 13, 14, 15, 16, 17, 108. Since (n = 9) (an odd number), the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{9+1}{2}=5) - th value, which is 14.

The median is less affected by the out - lier (108). The mean is pulled in the direction of the out - lier. So, the median works better as a measure of center in the presence of the out - lier.

Answer:

The mean is (25.111) The median is 14. The median works better as a measure of center here because the mean is affected by the outlier 108, while the median is not.