Question

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?

Answer 1

Answer:

As mean and median are equal, so the data will be in normal distribution in shape of a symmetrical "bell curve".

Step-by-step explanation:

The given data:   10   5   8   10   12   6   8   10   15   6   12   18

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".

Answer 2

Answer: C. the mean is equal to the median so the data is symmetrical.