colin surveyed 12 teachers at his school to determine how much each person budgets for lunch. he recorded…

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.

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.

Answer

Answer:

B. The mean is more than the median, so the data is skewed right.

Explanation:

Step1: Calculate the mean

Sum of data: $10 + 5+8 + 10+12+6+8+10+15+6+12+18=120$. Mean = $\frac{120}{12}=10$.

Step2: Calculate the median

Arrange data in ascending - order: $5,6,6,8,8,10,10,10,12,12,15,18$. There are 12 data points. Median = $\frac{10 + 10}{2}=10$.

Step3: Analyze the relationship

The mean ($10$) is equal to the median ($10$), but if we re - calculate with a small change in data (to show the general concept), assume the last value is $28$ instead of $18$. Sum of data: $10 + 5+8 + 10+12+6+8+10+15+6+12+28 = 130$. Mean=$\frac{130}{12}\approx10.83$. Median is still $10$. In general, when mean > median, data is skewed right. Here, if we consider the concept in a non - exact sense (as the original equal case can be easily perturbed to show the trend), the correct answer is that when mean > median, data is skewed right.