Question

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 __.

Answer 1

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**.