Comparing Data Distributions Practice

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An illustration shows two sets of dot plots. One is titled Movie 1 and the other is Movie 2. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Movie 1, a number line with arrows on both ends ranges from 17 to 43 in increments of 1. There is 1 dot above 17, 18, 21, 22, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, and 43. There are 2 dots above 23 and 3 dots above 20. For Movie 2, the number line ranges from 24 to 50 in increments of 1. There is 1 dot above 25, 28, 32, 35, 36, 42, 43, 45, 47, 48, and 50. There are 2 dots above 30, 34, and 37, and 3 dots above 40.

The dot plots show the ages, in years, of people watching two movies at a local theater. Find the median age of the people who watched each movie. Express your answer as a decimal if needed. Do not round your answer.

(1 point)
The median age of the people who watched Movie 1 is $$.
The median age of the people who watched Movie 2 is $$.
Incorrect

The median is the value in the middle. The height of the dots represents the frequency of each value. In Movie 1, there are three 20 year-olds. The Movie 1 dataset has an even number of values; therefore, calculate the average of the two middle numbers.
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Answer 1

To find the median ages of the people who watched Movie 1 and Movie 2, we need to first compile the ages from the dot plots and then determine the median for each movie.

Movie 1:

The ages and their frequencies from the dot plot for Movie 1 are:

• 17: 1
• 18: 1
• 20: 3
• 21: 1
• 22: 1
• 23: 2
• 25: 1
• 26: 1
• 28: 1
• 29: 1
• 32: 1
• 33: 1
• 35: 1
• 36: 1
• 38: 1
• 40: 1
• 43: 1

Now, let's list out all the ages based on their frequencies:

• 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, 43

Counting the number of ages gives us a total of 20. Since there is an even number of data points, the median will be the average of the two middle ages.

The middle ages are the 10th and 11th numbers in the ordered list.

• 10th: 25
• 11th: 26

Calculating the median: \[ \text{Median (Movie 1)} = \frac{25 + 26}{2} = \frac{51}{2} = 25.5 \]

Movie 2:

The ages and their frequencies from the dot plot for Movie 2 are:

• 24: 0
• 25: 1
• 28: 1
• 30: 2
• 32: 1
• 34: 2
• 35: 1
• 36: 1
• 40: 3
• 42: 1
• 43: 1
• 45: 1
• 47: 1
• 48: 1
• 50: 1

Now, let's list out the ages based on their frequencies:

• 25, 28, 30, 30, 32, 34, 34, 35, 36, 40, 40, 40, 42, 43, 45, 47, 48, 50

Counting the number of ages gives us a total of 18. Again, we have an even number of data points, so the median will be the average of the two middle ages.

The middle ages are the 9th and 10th numbers in the ordered list:

• 9th: 36
• 10th: 40

Calculating the median: \[ \text{Median (Movie 2)} = \frac{36 + 40}{2} = \frac{76}{2} = 38.0 \]

Final Answers:

• The median age of the people who watched Movie 1 is 25.5.
• The median age of the people who watched Movie 2 is 38.0.