Scenario 1: On Saturday, Kira stood outside the bowling alley from the time it opened until the time it closed. She asked the age of every 20th person entering the bowling alley for the whole day.

Data Set 1: 69, 10, 12, 11, 12, 1, 12, 13, 12, 16, 5, 35, 12, 36, 64, 10

1. Is the data taken from this bowling alley a random sample? Why or why not? Give as many details as possible.

Scenario 2: Two days later, on Monday evening, Kira went back to the bowling ally and asked the age of every 13th person entering the bowling alley.

Data Set 2: 25, 45, 56, 29, 65, 59, 62, 47, 36, 29, 55, 51, 37

2. What overlap exists between Data set 1 and 2?

1. For determining whether the data in Data Set 1 is a random sample, we need to consider several factors.

First, Kira asked the age of every 20th person entering the bowling alley. This implies that there was a predetermined pattern in selecting the individuals to ask, which means the sample was not randomly selected but instead followed a systematic sampling method.

Additionally, it's important to note that Kira was present at the bowling alley from the time it opened until the time it closed. This means that only people entering during that time frame were considered, potentially excluding individuals who arrived before or after Kira's observation period.

Furthermore, the fact that Kira stood outside the bowling alley and actively asked people their age introduces potential bias. People who were more likely to interact with Kira, or those who voluntarily provided their age, could differ from the overall population in terms of age distribution.

Considering all these factors, it can be concluded that the data in Data Set 1 is not a randomly selected sample, but rather a non-random sample with potential biases in selection and response.

2. To determine the overlap between Data Set 1 and Data Set 2, we need to compare the values present in both sets.

Comparing Data Set 1 and Data Set 2, we find the following ages: 12, 36.

Therefore, the overlap between Data Set 1 and Data Set 2 is the age 12 and the age 36. These two values are present in both sets.

1. It's a random sample of people at a bowling alley on a Saturday.

2. The overlap is the location -- the bowling alley.