Question

a local community center conducted a survey on the monthly earnings of teenagers who mow lawns in their neighborhoods. the data collected (in dollars) is as follows: {100, 120, 125, 130, 135, 140, 145, 150, 155, 160}. the mean of the data set is $131. what does this mean in the context of the scenario?
options:

• the lowest earning by a teenagers surveyed is $131.
• the average monthly earning of all teenagers surveyed is $131.
• the highest earning by a teenager surveyed is $131.
• all teenagers surveyed earn at least $131.

Explanation:

Step1: Recall the definition of mean

The mean (average) of a data set is calculated by summing all the values and dividing by the number of values. It represents the average value of the data set.

Step2: Analyze each option

• Option 1: The mean is not the lowest value. The lowest value here is $100$, so this is incorrect.
• Option 2: The mean is the average of the data set. So "The average monthly earning of all teenagers surveyed is $131$" correctly describes the mean.
• Option 3: The mean is not the highest value. The highest value here is $160$, so this is incorrect.
• Option 4: The mean does not represent the minimum value each teenager earns. Some earn less than $131$ (like $100$, $120$ etc.), so this is incorrect.

Answer:

The average monthly earning of all teenagers surveyed is $131$.