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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 for each movie, we first need to compile the ages based on the dot plots provided.

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

  • 17 → 1 dot
  • 18 → 1 dot
  • 20 → 3 dots
  • 21 → 1 dot
  • 22 → 1 dot
  • 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 count the total number of ages: 1 + 1 + 3 + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20 ages total.

To find the median, we need the middle value. As there are 20 ages (an even number), the median will be the average of the 10th and 11th values when arranged in ascending order.

Listing the ages in order, we get: 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, 43.

The 10th value is 25 and the 11th value is 26.

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

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

  • 24 → 0 dots
  • 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 count the total number of ages: 1 + 1 + 2 + 1 + 2 + 1 + 1 + 3 + 1 + 1 + 1 + 1 + 1 + 1 = 17 ages total.

For the median, as there are 17 values (an odd number), the median will be the 9th value when arranged in ascending order.

Listing the ages in order yields: 25, 28, 30, 30, 32, 34, 34, 35, 36, 40, 40, 40, 42, 43, 45, 47, 48, 50.

The 9th value is 36.

Therefore, the median for Movie 2 is: \[ \text{Median for Movie 2} = 36. \]

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 36.