Question

a new movie, beyond jupiter, is being released. the movie studio is asking 25 theaters to find the average age of those coming to see it on opening day. at each theater, as tickets are sold, every tenth person is asked their age until 15 people have been surveyed. this line plot shows the mean age of the moviegoers surveyed at each theater.
sample mean ages (years)
based on these statistics, what is the best estimate for the average age of people seeing beyond jupiter? complete the sentence.
the average age is likely to be about, though it could reasonably be anywhere between

Explanation:

Step1: List all sample mean ages

First, we identify each data point from the line plot:
32, 30, 31, 34, 30, 31, 32, 33, 30, 31, 32, 33, 30, 31, 32, 33, 30, 31, 32, 34, 30, 31, 35, 30, 39

Step2: Calculate the overall mean

Sum all values, then divide by 25 (total number of samples):
$$\text{Sum} = 32+30+31+34+30+31+32+33+30+31+32+33+30+31+32+33+30+31+32+34+30+31+35+30+39 = 825$$
$$\text{Mean} = \frac{825}{25} = 33$$

Step3: Identify the range of sample means

The smallest sample mean is 30, the largest is 39. A reasonable range for the true average is the interval around the overall mean that covers most sample values, so 31 to 35 (the central cluster of data points).

Answer:

The average age is likely to be about 33, though it could reasonably be anywhere between 31 and 35.