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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 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 quartile values.
The box plot displays the wrong quartile values.

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

1 answer

To analyze the box plot against the dataset \(19, 21, 23, 25, 27, 29\), we need to determine the five-number summary which consists of the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum.

  1. Minimum: The smallest value in the dataset is \(19\).
  2. Upper Quartile (Q3): This is the median of the upper half of the data. The upper half is \(25, 27, 29\). The median of these values is \(27\).
  3. Median: The median of the entire dataset \(19, 21, 23, 25, 27, 29\) is the average of \(23\) and \(25\), which is \(24\).
  4. Lower Quartile (Q1): This is the median of the lower half of the data \(19, 21, 23\). The median of these values is \(21\).
  5. Maximum: The largest value in the dataset is \(29\).

Now, let’s summarize:

  • Minimum: \(19\)
  • Q1: \(21\)
  • Median: \(24\)
  • Q3: \(27\)
  • Maximum: \(29\)

Checking the box plot:

  • The leftmost line (minimum) should be at \(19\),
  • The first box (Q1 to median) should extend from \(21\) to \(24\),
  • The second box (median to Q3) should extend from \(24\) to \(27\),
  • The rightmost line (maximum) should be at \(29\).

Identifying Errors:

  1. Minimum: Correctly shown as \(19\).
  2. Q1 and Median: The first box is incorrectly shown extending from \(22\) to \(24\) instead of \(21\) to \(24\), which indicates Q1 is wrong.
  3. Upper Quartile: The second box is correct extending from \(24\) to \(27\) but the second box doesn’t represent Q3 correctly.
  4. Maximum: Correctly shown as \(29\).

Given the discrepancies, particularly the issues with the lower quartile below its correct value, the most fitting response is:

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