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There are 20 classes at each of two middle schools. The number of students in each class at each school is shown in the dot plots below.

Number of Students in Each Class at Poplar Middle School
A dot plot titled Number of Students in Each Class at Poplar Middle School. A number line going from 20 to 29 labeled Number of students. There are 3 dots above 20, 5 above 21, 7 above 22, 4 above 23, 1 above 24, and 0 above 25, 26, 27, 28, and 29.

Number of Students in Each Class at Oak Middle School
A dot plot titled Number of Students in Each Class at Oak Middle School. A number line going from 20 to 29 labeled Number of students. There is 1 dot above 20, 2 above 21, 2 above 22, 4 above 23, 3 above 24, 2 above 25, 2 above 26, 2 above 27, 1 above 28, and 1 above 29.

What is the difference between the medians in the dot plots?
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1 answer

To find the difference between the medians of the two dot plots, we need to calculate the median for each school.

Poplar Middle School: The number of students in each class is represented in the dot plot as follows:

  • 3 classes with 20 students
  • 5 classes with 21 students
  • 7 classes with 22 students
  • 4 classes with 23 students
  • 1 class with 24 students

Now, we list all the class sizes in order by frequency:

  • 20, 20, 20 (3 times)
  • 21, 21, 21, 21, 21 (5 times)
  • 22, 22, 22, 22, 22, 22, 22 (7 times)
  • 23, 23, 23, 23 (4 times)
  • 24 (1 time)

So we have:

20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 24

There are 20 classes (even number), so the median will be the average of the 10th and 11th values:

  • 10th value is 22
  • 11th value is also 22

Median for Poplar = (22 + 22) / 2 = 22

Oak Middle School: The number of students in each class is represented as follows:

  • 1 class with 20 students
  • 2 classes with 21 students
  • 2 classes with 22 students
  • 4 classes with 23 students
  • 3 classes with 24 students
  • 2 classes with 25 students
  • 2 classes with 26 students
  • 2 classes with 27 students
  • 1 class with 28 students
  • 1 class with 29 students

Now, we list all class sizes in order by frequency:

  • 20 (1 time)
  • 21, 21 (2 times)
  • 22, 22 (2 times)
  • 23, 23, 23, 23 (4 times)
  • 24, 24, 24 (3 times)
  • 25, 25 (2 times)
  • 26, 26 (2 times)
  • 27, 27 (2 times)
  • 28 (1 time)
  • 29 (1 time)

So we have:

20, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 27, 27, 28, 29

There are 20 classes (even number), so the median will be the average of the 10th and 11th values:

  • 10th value is 24
  • 11th value is 24

Median for Oak = (24 + 24) / 2 = 24

Difference Between Medians: Now we find the difference between the medians of Poplar and Oak:

|Median of Poplar - Median of Oak| = |22 - 24| = 2

Thus, the difference between the medians is 2.

The answer is 2.