a number line shows the ages (in years) that people go to two different movies.

movie 1
1 1 0 3 1 1 2 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
movie 2
1 1 0 0 1 0 2 0 1 0 2 1 1 2 0 0 3 0 1 1 0 1 0 1 1 0 1
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The dot plots show the ages, in years, of people watching two movies at a local theater. Find the modal age of the people who watched each movie.

The model age of the people who watched Movie 1 is __.
The model age of the people who watched Movie 2 is __.

1 answer

To find the modal age for each movie, we need to identify the age (or ages) that occur most frequently in the given data.

Movie 1

The frequency of ages from the given data for Movie 1 is as follows:

  • Ages 17 to 43 are represented, and we can count the occurrences from the line above:
    • Age 17: 1
    • Age 18: 1
    • Age 19: 0
    • Age 20: 3
    • Age 21: 1
    • Age 22: 1
    • Age 23: 2
    • Age 24: 0
    • Age 25: 1
    • Age 26: 1
    • Age 27: 0
    • Age 28: 1
    • Age 29: 1
    • Age 30: 0
    • Age 31: 1
    • Age 32: 1
    • Age 33: 0
    • Age 34: 0
    • Age 35: 1
    • Age 36: 1
    • Age 37: 0
    • Age 38: 1
    • Age 39: 1
    • Age 40: 0
    • Age 41: 0
    • Age 42: 0
    • Age 43: 0

The highest frequency occurs for age 20, which has a count of 3. All other ages have lower or equal counts.

The modal age of the people who watched Movie 1 is 20.

Movie 2

Now we look at the frequency count for Movie 2:

  • Age 24: 1
  • Age 25: 1
  • Age 26: 0
  • Age 27: 0
  • Age 28: 1
  • Age 29: 2
  • Age 30: 1
  • Age 31: 1
  • Age 32: 2
  • Age 33: 0
  • Age 34: 1
  • Age 35: 1
  • Age 36: 0
  • Age 37: 0
  • Age 38: 1
  • Age 39: 1
  • Age 40: 1
  • Age 41: 0
  • Age 42: 0
  • Age 43: 0
  • Age 44: 0
  • Age 45: 0
  • Age 46: 0
  • Age 47: 0
  • Age 48: 0
  • Age 49: 0
  • Age 50: 0

The ages 29 and 32 both have a frequency of 2, which is the highest for this dataset.

The modal ages of the people who watched Movie 2 are 29 and 32.

Thus, the final answers are:

  • The modal age of the people who watched Movie 1 is 20.
  • The modal ages of the people who watched Movie 2 are 29 and 32.