Colin surveyed 12 teachers at school to determine how much each person budgets for lunch. He records his results in the table. What does the relationship between the mean and the median reveal about the shape of the data?

Mean is the simple average of all data. As, there are total 12 data, so the Mean will be: \(\frac{10+5+8+10+12+6+8+10+15+6+12+18}{12}= \frac{120}{12}=10\)

For finding the Median, first we need to rearrange the data according to the numerical order and then identify the middle value. So........

5 6 6 8 8 10 10 10 12 12 15 18

Here the middle values are 10 and 10. So, the median will be the average of those two middle values.

Thus, Median \(=\frac{10+10}{2}=\frac{20}{2}=10\)

We can see that, the relationship between the mean and the median is "they are equal". So, the data will be in normal distribution and the shape will be symmetrical "bell curve".

MrRoyal MrRoyal · Answer 2 · 2022-01-21T11:07:55-05:00

The data is a normal distribution and the shape will be symmetrical "bell curve".

The data elements are given as:

10, 5, 8, 10, 12, 6, 8, 10, 15, 6, 12, 18

Start by sorting the above data elements

5, 6, 6, 8, 8, 10, 10, 10, 12, 12, 15, 18

The mean of the dataset is then calculated as:

\(\bar x = \frac{5+ 6+ 6+ 8+ 8+ 10+ 10+ 10+ 12+ 12+ 15+ 18}{12}\)

\(\bar x = \frac{120}{12}\)

\(\bar x = 10\)

The median element is then calculated as:

\(Median = \frac{n + 1}{2}\ th\)

\(Median = \frac{12 + 1}{2}\ th\)

\(Median = \frac{13}{2}\ th\)

\(Median = 6.5\ th\)

This means that, the median is the average of the 6th and the 7th elements.

So, we have:

\(Median = \frac{10 + 10}{2}\)

\(Median = 10\)

So, we have:

\(\bar x = 10\)

\(Median = 10\)

When the mean and the median are equal, then

The data is a normal distribution
The shape will be symmetrical "bell curve".

Hence, the shape of the data is symmetrical bell curve

Read more about normal distributions at:

https://brainly.com/question/4079902