Question

jacob’s daily tips this work week were $99, $78, $58, $91, $90, and $68. is jacob correct in thinking that the median best represents how much money he makes in daily tips?
○ no, jacob is not correct. the mean amount he makes is $82.67 in a day.
○ yes, jacob is correct. the mean amount he makes is $81.67 in a day.
○ no, jacob is not correct. the median amount he makes is $86.00 in a day.
○ yes, jacob is correct. the median amount he makes is $84.00 in a day.

Explanation:

Step1: Sort the data

First, sort the data set \(\{99,78,58,91,90,68\}\) in ascending order: \(\{58,68,78,90,91,99\}\).

Step2: Calculate the median

Since there are \(n = 6\) (an even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values. \(\frac{n}{2}=3\) and \(\frac{n}{2}+1 = 4\). The third - value is \(78\) and the fourth - value is \(90\). The median \(M=\frac{78 + 90}{2}=\frac{168}{2}=84\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n = 6\). \(\sum_{i=1}^{6}x_{i}=99+78+58+91+90+68=484\). The mean \(\bar{x}=\frac{484}{6}\approx80.67\).

Answer:

Yes, Jacob is correct. The median amount he makes is \(\$84.00\) in a day.