Question

Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch. He recorded his results in the table.
A 6-column table with 2 rows. The first row contains entries 10, 5, 8, 10, 12, 6. The second row contains entries 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 1

Answer:

"The mean is equal to the median, so the data is symmetrical" is the correct  relationship between the mean and median about the shape of the data.

Step-by-step explanation:

As the table is given by

10          5          8          10          12          6

8           10         15          6          12          18

So fetching the data from the table

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

Calculating the mean

$Mean= \frac{10+5+8+10+12+6+8+10+15+6+12+18}{12}$

$Mean= 10$

Rearranging the data in ascending order will be

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

Calculating the median

$Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{10+10}{2}=10$

As we can that

$Mean = Median$

So, we can conclude that as the mean is equal to the median, so the data is symmetrical.

Therefore, "The mean is equal to the median, so the data is symmetrical" is the correct  relationship between the mean and median about the shape of the data.

Keywords: data distribution, median , mean, symmetrical data

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Answer 2

Answer:

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

Step-by-step explanation:

The given table is

First row: 10, 5, 8, 10, 12, 6.

Second row: 8, 10, 15, 6, 12, 18.

To find the right answer, we need to calculate the mean the the median of this data set.

$x=\frac{\sum x_{i} }{N}=\frac{10+5+8+10+12+6+8+10+15+6+12+18}{12}=\frac{120}{12}=10$

The mean of the data set is 10.

Now, to find the median, first, we need to arrange the data set from least to greatest.

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

Notice that the middle is between 10 and 10,

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

Therefore, the median and the mean are equal, both are equal to 10.

When this happens, it means the data set is symmetrical, its box plots would be symmetrical. So, the right answer is the third choice.