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An illustration shows a number line ranging from 19 to 29 in increments of 1. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 22 to 24 and the second box extends from 24 to 26. A line extends from 19 to the left side of the first box. Another line extends from the right side of the second box to 29.

The dataset for this box plot is 19, 21, 23, 25, 27, 29. What is the error on the box plot?

(1 point)
Responses

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

The box plot displays the wrong quartile values.

1 answer

To determine if there are any errors in the box plot provided, we first need to calculate the values for the minimum, maximum, median, lower quartile (Q1), and upper quartile (Q3) of the given dataset: 19, 21, 23, 25, 27, 29.

  1. Minimum: The smallest number in the dataset is 19.
  2. Maximum: The largest number in the dataset is 29.
  3. Median: The median is the average of the two middle numbers (when the dataset is sorted). The two middle numbers here are 23 and 25, so the median is (23 + 25) / 2 = 24.
  4. Lower Quartile (Q1): This is the median of the lower half of the data (19, 21, 23). The median of this subset is 21.
  5. Upper Quartile (Q3): This is the median of the upper half of the data (25, 27, 29). The median of this subset is 27.

Now we outline the key values:

  • Minimum = 19
  • Lower Quartile (Q1) = 21
  • Median = 24
  • Upper Quartile (Q3) = 27
  • Maximum = 29

Now, examining the box plot:

  • The first box extends from 22 to 24. This means the lower quartile would be displayed incorrectly, as we calculated Q1 to be 21, not 22.
  • The second box extends from 24 to 26. The median, according to our calculations, is 24, but this creates confusion about the upper quartile (Q3), which should be noted at 27 rather than 26.

Thus, we conclude that the box plot displays the wrong lower quartile (Q1, which should be 21 instead of 22) and the upper quartile (Q3, which should be 27 instead of 26).

The correct answer is:

The box plot displays the wrong lower quartile and maximum values.