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

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

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

1 answer

To analyze the box plot and its representation of the dataset (71, 72, 73, 74, 75, 76, 77, 78), we need to find the correct minimum, maximum, median, and quartiles based on this dataset:

  1. Minimum Value (Min): 71
  2. Maximum Value (Max): 78
  3. Median: Since there are 8 values, the median will be the average of the 4th and 5th values: (74 + 75) / 2 = 74.5
  4. Upper Quartile (Q3): The upper quartile (the median of the upper half of the data) in this case is the average of 76 and 77: (76 + 77) / 2 = 76.5
  5. Lower Quartile (Q1): The lower quartile (the median of the lower half of the data) is the average of 72 and 73: (72 + 73) / 2 = 72.5

Based on the box plot description:

  • The left whisker starts at the minimum value of 71 (correct).
  • The first box extends from Q1 (72.5) to Q2 (74) (correct).
  • The second box extends from Q2 (74) to Q3 (76.5) (correct).
  • The right whisker ends at the maximum value of 78 (correct).

The box plot appears to represent the minimum correctly, the maximum correctly, and the median correctly, but Q2 is noted as 74 when it should be 74.5 according to the calculations.

Given this analysis:

  • The box plot displays the wrong median.

Therefore, the correct answer is:

The box plot displays the wrong median.