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 39. (type an integer or a decimal. do not round.) the median is □. (type an integer or a decimal. do not round.)

Explanation:

Part (b) - Finding the Median after replacing 33 with 123

Step1: List the new data set

After replacing 33 with 123, the data set becomes \(25, 26, 27, 28, 29, 30, 31, 32, 123\).

Step2: Determine the number of data points

There are \(n = 9\) data points (odd number of observations).

Step3: Find the middle position

For \(n\) odd, the median is the value at the position \(\frac{n + 1}{2}\). Here, \(\frac{9+ 1}{2}=5\)-th position.

Step4: Identify the 5th value

Arranging the data in ascending order (it's already in order), the 5th value is \(29\).

Answer:

The median is \(29\).