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An illustration shows a number line ranging from 71 to 78 in increments of 1. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 72.5 to 74 and the second box extends from 74 to 76.5. A line extends from 71 to the left side of the first box. Another line extends from the right side of the second box to 78.

The dataset for this box plot is 71, 72, 73, 74, 75, 76, 77, 78. What is the error on the box plot?

(1 point)
Responses

The box plot displays the wrong median and upper quartile.
The box plot displays the wrong median and upper quartile.

The box plot displays the wrong minimum and maximum values.
The box plot displays the wrong minimum and maximum values.

The box plot displays the wrong median.
The box plot displays the wrong median.

The box plot displays the wrong minimum value.
The box plot displays the wrong minimum value.
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1 answer

To evaluate the accuracy of the box plot given the dataset 71, 72, 73, 74, 75, 76, 77, 78, we need to determine the correct values for the minimum, maximum, median, and quartiles:

  1. Minimum Value: 71
  2. Maximum Value: 78
  3. Median: To find the median, we calculate the average of the two middle values (74 and 75), which gives us \( \frac{74 + 75}{2} = 74.5 \).
  4. Lower Quartile (Q1): This is the median of the first half of the dataset (71, 72, 73, 74). The median is 72.5.
  5. Upper Quartile (Q3): This is the median of the second half (75, 76, 77, 78). The median is 76.5.

From the box plot:

  • The first box extends from 72.5 to 74, which corresponds to the lower quartile and a value that is part of the dataset, so this part is correct.
  • The second box extends from 74 to 76.5, which is the median (74.5) to upper quartile (76.5); however, it incorrectly includes 74 as the starting point of the second box instead of the median.

Given these observations, the box plot does not display the correct median because the median (74.5) is not properly represented. Additionally, the upper quartile is correctly represented, but since the question asks for the error regarding the median, the best choice here is:

The box plot displays the wrong median.