Question

consider the data set 25,26,27,28,29,30,31,32,33. complete parts (a) through (c) below. a. obtain the mean and median of the data. the mean is 29 . (type an integer or a decimal. do not round.) the median is 29 . (type an integer or a decimal. do not round.) b. replace the 33 in the data set by 123 and again compute the mean and median. decide which measure of center works better here, and explain your answer. the mean is \boxed{} (type an integer or a decimal. do not round.)

Explanation:

Step1: Find the sum of the new data set

The original data set is 25,26,27,28,29,30,31,32,33. After replacing 33 with 123, the new data set is 25,26,27,28,29,30,31,32,123. First, find the sum of the original data set: \(25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33\). We know from part (a) that the sum of the original data set is \(9\times29 = 261\) (since the mean was 29 and there are 9 data points). Now, we replaced 33 with 123, so the new sum is \(261 - 33 + 123\). Calculate that: \(261 - 33 = 228\), then \(228 + 123 = 351\).

Step2: Calculate the new mean

The mean is the sum of the data set divided by the number of data points. There are still 9 data points. So the mean is \(\frac{351}{9}\).
\(\frac{351}{9}=39\)

Answer:

39