Question

the number of credits being taken by a sample of 13 full - time college students are listed below. find the mean, median, and mode of the data. if possible, if any measure cannot be found or does not represent the center of the data, explain why.
4 4 7 7 4 5 3 3 3 3 6 25
(type an integer or decimal rounded to one decimal place as needed.)
a. the data set does not have a mean.
does the mean represent the center of the data?
a. the mean represents the center.
b. the mean does not represent the center because it is not a data value.
c. the mean does not represent the center because it is the largest data value.
d. the mean does not represent the center because it is the smallest data value.
e. the data set does not have a mean.
find the median. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the median is 4.
(type an integer or decimal rounded to one decimal place as needed.)
b. the data set does not have a median.
does the median represent the center of the data?
a. the median represents the center.
b. the median does not represent the center because it is the smallest data value.
c. the median does not represent the center because it is not a data value.
d. the median does not represent the center because it is the largest data value.
e. the data set does not have a median.

Explanation:

Step1: Organize data

First, organize the data set \(4,4,7,7,4,5,3,3,3,3,6,25\) in ascending - order: \(3,3,3,3,4,4,4,5,6,7,7,25\).

Step2: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 12\) and \(\sum_{i=1}^{12}x_{i}=3\times4 + 4\times3+5 + 6+7\times2 + 25=12 + 12+5 + 6+14 + 25=74\). So, \(\bar{x}=\frac{74}{12}\approx6.2\). The mean represents the center of the data in a sense as it is the average value of all data points.

Step3: Calculate the median

Since \(n = 12\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data values. \(\frac{n}{2}=6\) and \(\frac{n}{2}+1 = 7\). The 6th value is \(4\) and the 7th value is \(4\), so the median \(M=\frac{4 + 4}{2}=4\). The median represents the center of the data as it divides the data set into two equal - sized halves.

Step4: Calculate the mode

The mode is the data value that appears most frequently. In the data set, the number \(3\) appears \(4\) times, more frequently than any other number, so the mode is \(3\).

Answer:

Mean: \(6.2\), represents the center as it is the average.
Median: \(4\), represents the center as it divides data into two equal - sized halves.
Mode: \(3\), represents the most frequently occurring value.