Question

consider the data set 11,12,13,14,15,16,17,18,19. complete parts (a) through (c) below. a. obtain the mean and median of the data. the mean is 15. (type an integer or a decimal. do not round.) the median is 15. (type an integer or a decimal. do not round.) b. 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. the mean is . (type an integer or a decimal. do not round.)

Explanation:

Step1: Calculate new sum

The original data set sum is \(11 + 12+13+14+15+16+17+18+19=135\). After replacing 19 with 109, the new sum is \(135 - 19+109=225\).

Step2: Calculate new mean

There are 9 data - points. The new mean is \(\frac{225}{9}=25\).

Step3: Determine new median

The data set after replacement is \(11,12,13,14,15,16,17,18,109\). Since there are 9 (an odd number) data - points, the median is the 5th value when the data is arranged in ascending order, which is 15.

Step4: Analyze better measure

The median is a better measure of center here. The mean is affected by the outlier (109), while the median remains the same as it only depends on the middle - value of the ordered data set and is not influenced by extreme values.

Answer:

The mean is 25.
The median is 15.
The median is a better measure of center.