There are twenty 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. 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. 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.

Which statement correctly compares the mean number of students for the data in the plots?
There are about 2 more students in each class at Poplar Middle School than at Oak Middle School.
There are about 2 more students in each class at Oak Middle School than at Poplar Middle School.
There are about 5 more students in each class at Poplar Middle School than at Oak Middle School.
There are about 5 more students in each class at Oak Middle School than at Poplar Middle School.

1 answer

To find the mean number of students in each class at Poplar Middle School and Oak Middle School, we need to calculate the total number of students at each school and divide by the number of classes (20).

Poplar Middle School:

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

Calculating the total number of students: \[ (20 \times 3) + (21 \times 5) + (22 \times 7) + (23 \times 4) + (24 \times 1) \] \[ = 60 + 105 + 154 + 92 + 24 = 435 \]

Mean for Poplar Middle School: \[ \text{Mean} = \frac{435}{20} = 21.75 \]


Oak Middle School:

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

Calculating the total number of students: \[ (20 \times 1) + (21 \times 2) + (22 \times 2) + (23 \times 4) + (24 \times 3) + (25 \times 2) + (26 \times 2) + (27 \times 2) + (28 \times 1) + (29 \times 1) \] \[ = 20 + 42 + 44 + 92 + 72 + 50 + 52 + 54 + 28 + 29 = 431 \]

Mean for Oak Middle School: \[ \text{Mean} = \frac{431}{20} = 21.55 \]


Comparison:

  • Mean for Poplar: 21.75
  • Mean for Oak: 21.55

To find the difference, we subtract the mean of Oak from the mean of Poplar: \[ 21.75 - 21.55 = 0.2 \]

Poplar has about 0.2 more students per class than Oak.

Conclusion:

None of the statements provided are accurate since the comparison shows that Poplar Middle School has about 0.2 more students than Oak Middle School. The correct interpretation would be that Poplar has slightly more students, but it does not align with any of the options given.