Question

the dot - plot represents the distribution of wages earned during a one - week period by 12 college students.
112 114 116 118 120 122 124
weekly wages (dollars)

1. what is the mean? interpret this value based on the situation.

the mean is $______. this means that if all 12 students put their earnings for the week together and then redistributed the money ______ (differently, equally) each person would get $______.

1. what is the median? interpret this value based on the situation.

the median is $______. this means that ______ (half, all) of the students earned $____ or more, and __ (half, none) earned $____ or less.

1. would a box plot of the same data have allowed you to find both the mean and the median? answer with yes or no

mean? ______
median? ______

Explanation:

Step1: Count data - point frequencies

From the dot - plot: 112 has 1 dot, 114 has 1 dot, 116 has 3 dots, 118 has 2 dots, 120 has 2 dots, 124 has 3 dots.

Step2: Calculate the sum of all data points

\[S=(112\times1)+(114\times1)+(116\times3)+(118\times2)+(120\times2)+(124\times3)\]
\[S = 112+114 + 348+236+240+372\]
\[S=1422\]

Step3: Calculate the mean

The number of data points \(n = 12\). The mean \(\bar{x}=\frac{S}{n}=\frac{1422}{12}=118.5\).

Step4: Find the median

Since \(n = 12\) (an even number), the median is the average of the \(\frac{n}{2}=6\)th and \((\frac{n}{2}+1) = 7\)th ordered data - points. Ordering the data: 112, 114, 116, 116, 116, 118, 118, 120, 120, 124, 124, 124. The 6th value is 118 and the 7th value is 118, so the median \(M=\frac{118 + 118}{2}=118\).

Step5: Analyze box - plot capabilities

A box - plot shows the median (the line inside the box), but not the mean.

Answer:

Blank 1: 118.5
Blank 2: equally
Blank 3: 118.5
Blank 4: 118
Blank 5: half
Blank 6: 118
Blank 7: half
Blank 8: 118
Blank 9: No
Blank 10: Yes