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.\n10 5 8 10 12 6\n8 10 15 6 12 18\nwhat does the relationship between the mean and median reveal about the shape of the data?\nthe mean is less than the median, so the data is skewed left.\nthe mean is more than the median, so the data is skewed right.\nthe mean is equal to the median, so the data is symmetrical.\nthe 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.\n10 5 8 10 12 6\n8 10 15 6 12 18\nwhat does the relationship between the mean and median reveal about the shape of the data?\nthe mean is less than the median, so the data is skewed left.\nthe mean is more than the median, so the data is skewed right.\nthe mean is equal to the median, so the data is symmetrical.\nthe mean is equal to the median, so the data is linear.

Answer

Answer:

  1. First, arrange the data in ascending - order: $5,6,6,8,8,10,10,10,12,12,15,18$.
  2. Calculate the median:
    • Since $n = 12$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data 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 $M=\frac{10 + 10}{2}=10$.
  3. Calculate the mean:
    • The sum of the data values is $5+6+6+8+8+10+10+10+12+12+15+18=110$.
    • The mean $\bar{x}=\frac{110}{12}\approx9.17$.
  4. Analyze the relationship:
    • Since the mean ($\approx9.17$) is less than the median ($10$), the data is skewed left. So the answer is: The mean is less than the median, so the data is skewed left.

Explanation:

Step1: Arrange data

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

Step2: Calculate median

$M=\frac{10 + 10}{2}=10$

Step3: Calculate mean

$\bar{x}=\frac{5 + 6+6+8+8+10+10+10+12+12+15+18}{12}=\frac{110}{12}\approx9.17$

Step4: Analyze relationship

Mean ($\approx9.17$) < Median ($10$), data is skewed left.