Question

colin surveyed 12 teachers at his school to determine how much each person budgets for lunch. he recorded his results in the table.

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

what does the relationship between the mean and median reveal about the shape of the data?
the mean is less than the median, so the data is skewed left.
the mean is more than the median, so the data is skewed right.
the mean is equal to the median, so the data is symmetrical.
the mean is equal to the median, so the data is linear.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{10 + 5+8+10+12+6+8+10+15+6+12+18}{12}=\frac{120}{12} = 10$.

Step2: Calculate the median

First, order the data: $5,6,6,8,8,10,10,10,12,12,15,18$. Since $n = 12$ (even), the median $M=\frac{10 + 10}{2}=10$.

Step3: Analyze the relationship

Since the mean ($10$) is equal to the median ($10$), the data is symmetrical.

Answer:

The mean is equal to the median, so the data is symmetrical.