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

Question

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
0 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 median age of the people who watched each movie.

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

Answer 1

To find the median age of the people who watched each movie, we first need to determine the total frequency of ages indicated in the dot plots for each movie.

Movie 1

Here is the age frequency breakdown based on the provided data:

• 17: 1
• 18: 1
• 19: 0
• 20: 3
• 21: 1
• 22: 1
• 23: 2
• 24: 0
• 25: 1
• 26: 1
• 27: 0
• 28: 1
• 29: 1
• 30: 0
• 31: 1
• 32: 1
• 33: 0
• 34: 1
• 35: 1
• 36: 0
• 37: 1
• 38: 1
• 39: 0
• 40: 1
• 41: 0
• 42: 1
• 43: 0

Now, we tally the total number of attendees: 1 + 1 + 0 + 3 + 1 + 1 + 2 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 1 + 0 + 0 + 1 = 29.

The sorted ages for Movie 1 (based on the counts) are as follows:

• 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 42,

To find the median of 29 attendees:

• The median is the middle value. Since the total count is odd (29), the median is the 15th value in the sorted list.

Counting to the 15th value:

1. 17
2. 18
3. 20
4. 20
5. 20
6. 21
7. 22
8. 23
9. 23
10. 25
11. 26
12. 28
13. 29
14. 31
15. 32 (the median for Movie 1)

Movie 2

Next, we sum the ages from Movie 2 frequency data:

• 24: 0
• 25: 1
• 26: 0
• 27: 1
• 28: 0
• 29: 2
• 30: 0
• 31: 1
• 32: 2
• 33: 1
• 34: 1
• 35: 0
• 36: 1
• 37: 0
• 38: 0
• 39: 3
• 40: 0
• 41: 1
• 42: 1
• 43: 0
• 44: 1
• 45: 0
• 46: 0
• 47: 0
• 48: 1
• 49: 0
• 50: 0

Totaling the counts: 0 + 1 + 0 + 1 + 0 + 2 + 0 + 1 + 2 + 1 + 1 + 0 + 1 + 0 + 0 + 3 + 0 + 1 + 1 + 0 + 1 + 0 + 0 + 0 + 1 + 0 + 0 = 20.

Sorting the ages: The ages sorted based on the counts for the total of 20 attendees are:

• 25, 27, 29, 29, 31, 32, 32, 33, 34, 36, 39, 39, 39, 41, 42, 44, 48

To find the median of 20 people:

• The median is the average of the 10th and 11th values.

Counting to find the 10th and 11th values:

1. 25
2. 27
3. 29
4. 29
5. 31
6. 32
7. 32
8. 33
9. 34
10. 36 (10th value)
11. 39 (11th value)

Now calculate the median: \[ \text{Median} = \frac{36 + 39}{2} = 37.5 \]

Final Results

• The median age of the people who watched Movie 1 is 32.
• The median age of the people who watched Movie 2 is 37.5.