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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
.
Remaining Attempts : 3
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1 answer

To find the median age of the people who watched each movie, we need to determine the total number of data points (ages) for each movie and then identify the middle value.

Movie 1:

The ages of individuals watching Movie 1 based on the dot plot are as follows:

  • 1 dot at age 17
  • 1 dot at age 18
  • 3 dots at age 20
  • 2 dots at age 23
  • 1 dot at age 21
  • 1 dot at age 22
  • 1 dot at age 25
  • 1 dot at age 26
  • 1 dot at age 28
  • 1 dot at age 29
  • 1 dot at age 32
  • 1 dot at age 33
  • 1 dot at age 35
  • 1 dot at age 36
  • 1 dot at age 38
  • 1 dot at age 40
  • 1 dot at age 43

Counting the dots:

  • Total: 1 (17) + 1 (18) + 3 (20) + 2 (23) + 1 (21) + 1 (22) + 1 (25) + 1 (26) + 1 (28) + 1 (29) + 1 (32) + 1 (33) + 1 (35) + 1 (36) + 1 (38) + 1 (40) + 1 (43) = 19 ages.

To find the median:

  • Arrange the ages in increasing order:
    • 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, 43
  • The median is the middle number in sorted data. Since there are 19 data points, the median is the 10th age.
  • The 10th value is 25.

Median for Movie 1: 25.

Movie 2:

The ages for Movie 2 based on the dot plot are as follows:

  • 1 dot at age 25
  • 1 dot at age 28
  • 2 dots at age 30
  • 1 dot at age 32
  • 2 dots at age 34
  • 2 dots at age 35
  • 2 dots at age 36
  • 3 dots at age 40
  • 1 dot at age 42
  • 3 dots at age 43
  • 1 dot at age 45
  • 1 dot at age 47
  • 1 dot at age 48
  • 1 dot at age 50

Counting the dots:

  • Total: 1 (25) + 1 (28) + 2 (30) + 1 (32) + 2 (34) + 2 (35) + 2 (36) + 3 (40) + 1 (42) + 3 (43) + 1 (45) + 1 (47) + 1 (48) + 1 (50) = 19 ages.

To find the median:

  • Arrange the ages in increasing order:
    • 25, 28, 30, 30, 32, 34, 34, 35, 35, 36, 36, 40, 40, 40, 42, 43, 43, 43, 45, 47, 48, 50
  • The median is the 10th age from the sorted list:
    • The 10th value is 36.

Median for Movie 2: 36.

Summary:

  • The median age of the people who watched Movie 1 is 25.
  • The median age of the people who watched Movie 2 is 36.