Question

find the mean, median, and mode of the data, if possible. if any of these measures cannot be found or a measure does not represent the center of the data, explain why. a sample of seven admission test scores for a professional school are listed below. 11.8 11.3 10.7 11.8 10.6 10.5 11.8

a. the median score is
(round to one decimal place as needed.)
b. there is no median score.

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 largest 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 smallest data value.

what is the mode of the scores? select the correct choice below and fill in any answer box to complete your choice.

a. the mode(s) of the scores is (are)
(use a comma to separate answers as needed.)
b. there is no mode.

does (do) the mode(s) represent the center of the data?

a. the mode(s) represent(s) the center.
b. the mode(s) cant represent the center because it (they) is (are) not a data value.
c. the mode(s) does (do) not represent the center because it (one) is the smallest data value.
d. the mode(s) does (do) not represent the center because it (one) is the largest data value.

Explanation:

Step1: Order the data

First, we order the data set: \(10.5, 10.6, 10.7, 11.3, 11.8, 11.8, 11.8\)

Step2: Find the median

Since there are \(n = 7\) (odd number of data points), the median is the middle value, which is the \(\frac{7 + 1}{2}=4^{th}\) value. The \(4^{th}\) value in the ordered data is \(11.3\).

Step3: Analyze if median represents the center

The median is the middle value of the ordered data, so it should represent the center as it divides the data into two equal halves.

Step4: Find the mode

The mode is the value that appears most frequently. Here, \(11.8\) appears three times, more than any other value.

Step5: Analyze if mode represents the center

The mode \(11.8\) is the most frequent value. Since it is in the upper half of the ordered data (but still, as a measure of center, the mode can represent the center in terms of the most common value, and in this case, since it's a repeated value in the data set, it does represent a central tendency in terms of frequency).

Answer:

• Median score: \(11.3\) (Option A for median calculation, Option A for median representing the center)
• Mode of the scores: \(11.8\) (Option A for mode calculation, Option A for mode representing the center)