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: 69, 10, 12, 11, 12, 1, 12, 13, 12, 16, 5, 35, 12, 36, 64, 10
7. Is the data taken from this bowling alley a random sample? Why or why not? Give as many details as possible.
6. Show all the steps (or calculations) you need to find the RANGE of the data set.
9A. What's the lower quartile?
9B. What's the upper quartile?
9C. What's the interquartile range?
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: 25, 45, 56, 29, 65, 59, 62, 47, 36, 29, 55, 51, 37
11A. What overlap exists between these two sets of data?
11B. What's the interquartile range?
please help! my brain isn't working today
I only need help with, 7 and 11A now
7. To determine if the data taken from the bowling alley is a random sample, we need to consider a few factors. In this scenario, Kira asked the age of every 20th person entering the bowling alley on Saturday and every 13th person on Monday. Random sampling typically involves selecting individuals from a population without any specific pattern or bias. In this case, asking the age of every 20th or 13th person indicates a systematic sampling method rather than a completely random one.
Additionally, there could be potential bias in the sample selection process. For example, if the entrance to the bowling alley is near a specific location or if there are specific events taking place on those particular days, it could influence the age distribution of those entering the bowling alley. Therefore, the data is not likely to represent a random sample due to the systematic selection method and potential bias.
6. To find the range of a data set, you simply subtract the smallest value from the largest value in the set. For the given data set: 69, 10, 12, 11, 12, 1, 12, 13, 12, 16, 5, 35, 12, 36, 64, 10
Step 1: Arrange the data set in ascending order: 1, 5, 10, 10, 11, 12, 12, 12, 12, 13, 16, 35, 36, 64, 69
Step 2: Subtract the smallest value (1) from the largest value (69): 69 - 1 = 68
Therefore, the range of this data set is 68.
9A. To find the lower quartile (Q1), we need to determine the median of the lower half of the data set.
Step 1: Arrange the data set in ascending order: 1, 5, 10, 10, 11, 12, 12, 12, 12, 13, 16, 35, 36, 64, 69
Step 2: Calculate the position of Q1: (n+1) / 4, where n is the total number of data points. In this case, n = 16, so (16+1) / 4 = 4th position.
Step 3: Find the value at the 4th position, which is 10.
Therefore, the lower quartile (Q1) is 10.
9B. To find the upper quartile (Q3), we need to determine the median of the upper half of the data set.
Step 1: Arrange the data set in ascending order: 1, 5, 10, 10, 11, 12, 12, 12, 12, 13, 16, 35, 36, 64, 69
Step 2: Calculate the position of Q3: 3(n+1) / 4, where n is the total number of data points. In this case, n = 16, so 3(16+1) / 4 = 13th position.
Step 3: Find the value at the 13th position, which is 36.
Therefore, the upper quartile (Q3) is 36.
9C. The interquartile range (IQR) is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3).
In this case, IQR = Q3 - Q1 = 36 - 10 = 26.
11A. To find the overlap between the two data sets, we need to examine the values that are present in both data sets.
The first data set consists of: 69, 10, 12, 11, 12, 1, 12, 13, 12, 16, 5, 35, 12, 36, 64, 10
The second data set consists of: 25, 45, 56, 29, 65, 59, 62, 47, 36, 29, 55, 51, 37
From analyzing the two data sets, we find that the number 36 appears in both sets.
11B. The interquartile range (IQR) for the second data set can be calculated in the same manner as before.
Step 1: Arrange the data set in ascending order: 25, 29, 29, 36, 37, 45, 47, 51, 55, 56, 59, 62, 65
Step 2: Calculate Q1: (13+1) / 4 = 3rd position, which is 29.
Step 3: Calculate Q3: 3(13+1) / 4 = 10th position, which is 56.
Step 4: Calculate IQR = Q3 - Q1 = 56 - 29 = 27.
Therefore, the interquartile range for the second data set is 27.