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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
.

1 answer

To find the median age of the people who watched each movie, we need to first list out all of the ages represented by the dots in each plot, then determine the median from those lists.

Movie 1 Plot

From the description, we can count the ages and frequency from Movie 1:

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

Now we can compile the ages in a sorted format:

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

Counting the total number of data points:

  • Total = 21

Since there are 21 data points (an odd number), the median will be the middle value, which is at position \( \frac{21 + 1}{2} = 11 \).

The 11th value in the sorted list is 23.

Movie 2 Plot

Now we can count the ages from Movie 2:

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

Now we can sort and list the ages:

\[ 25, 28, 30, 30, 32, 34, 34, 35, 36, 40, 40, 40, 42, 43, 45, 47, 48, 50 \]

Counting the total number of data points:

  • Total = 18

Since there are 18 data points (an even number), the median will be the average of the two middle values, which are at positions 9 and 10.

The 9th value is 36, and the 10th value is 40. Thus, the median is:

\[ \text{Median} = \frac{36 + 40}{2} = \frac{76}{2} = 38 \]

Final Answers

  • The median age of the people who watched Movie 1 is 23.
  • The median age of the people who watched Movie 2 is 38.