Question

the list below shows the prices of t - shirts at a clothing store.
{8, 10, 10, 12, 15, 15, 18}
which statement best describes the mean of this set?
○ the difference between the least and greatest prices
○ the sum of the prices
○ the quotient of the difference between the least and greatest prices divided by 7
○ the sum of the prices divided by 7

Explanation:

Step1: Recall the formula for the mean

The mean (average) of a set of numbers is calculated by taking the sum of all the numbers in the set and then dividing that sum by the number of elements in the set.

Step2: Analyze the given set

The set of T - shirt prices is \(\{8, 10, 10, 12, 15, 15, 18\}\). The number of elements (T - shirt prices) in this set is \(n = 7\).

Step3: Evaluate each option

• Option 1: The difference between the least and greatest prices is the range, not the mean. The range is \(18 - 8=10\), so this is incorrect.
• Option 2: The sum of the prices is just the total of all the values, not the mean. We need to divide the sum by the number of values to get the mean, so this is incorrect.
• Option 3: The quotient of the difference between the least and greatest prices (range) divided by 7 is not the formula for the mean. The range divided by the number of elements does not give the mean, so this is incorrect.
• Option 4: The sum of the prices divided by 7. Since the mean is calculated as \(\text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}\) and the number of values here is 7, this is the correct formula for the mean.

Answer:

the sum of the prices divided by 7