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

First, find the sum of the data values: $10 + 5+8 + 10+12 + 6+8+10+15+6+12+18=120$. There are $n = 12$ data - points. The mean $\bar{x}=\frac{120}{12}=10$.

Step2: Calculate the median

Arrange the data in ascending order: $5,6,6,8,8,10,10,10,12,12,15,18$. Since $n = 12$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. The 6th value is $10$ and the 7th value is $10$, so the median $M=\frac{10 + 10}{2}=10$.

Step3: Analyze the relationship

The mean $\bar{x}=10$ and the median $M = 10$. When the mean is equal to the median, the data is symmetrical.

Answer:

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