Use the image to answer the question.

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
Please help me it's not 23 and 38 please give the right answer

1 answer

To find the median ages of the people who watched each movie, we will first summarize the data from the dot plots for Movies 1 and 2, count the total number of viewers, and then determine the median.

Movie 1:

The data can be listed as follows, based on the dot representations:

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, counting the dots gives us:

Number of viewers = 1 + 1 + 3 + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 17 viewers.

To find the median:

The ages, when sorted, are: 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, 43.
The median position for 17 viewers (odd number) is at position \( \frac{17 + 1}{2} = 9 \) (9th position).
The sorted list: 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, 43.

Thus, the median age for Movie 1 is 23.

Movie 2:

The data for Movie 2 is as follows:

24: 0 dots
25: 1 dot
28: 1 dot
30: 2 dots
32: 1 dot
34: 2 dots
35: 1 dot
36: 1 dot
37: 2 dots
40: 3 dots
42: 1 dot
43: 1 dot
45: 1 dot
47: 1 dot
48: 1 dot
50: 1 dot

Counting the dots gives us:

Number of viewers = 1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 + 2 + 3 + 1 + 1 + 1 + 1 + 1 + 1 = 16 viewers.

To find the median:

The ages (sorted) are: 25, 28, 30, 30, 32, 34, 34, 35, 36, 37, 37, 40, 40, 40, 42, 43, 45, 47, 48, 50.
The median position for 16 viewers (even number) is at positions \( \frac{16}{2} = 8 \) and \( \frac{16}{2} + 1 = 9 \) (8th and 9th positions).
The sorted list: 25, 28, 30, 30, 32, 34, 34, 35, 36, 37, 37, 40, 40, 40, 42, 43, 45, 47, 48, 50.

The median calculation:

The average of the 8th and 9th values: \( \frac{35 + 36}{2} = 35.5 \).

Thus, the median age for Movie 2 is 35.5.

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 35.5.