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An illustration shows a number line ranging from 43 to 48 in increments of 1. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 45 to 45.5 and the second box extends from 45.5 to 46. A line extends from 43 to the left side of the first box. Another line extends from the right side of the second box to 48.

The dataset for this box plot is 43, 44, 45, 46, 47, 48. What is the error on the box plot?

(1 point)
Responses

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

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

The box plot displays the wrong median and upper quartile.

1 answer

To determine the error in the box plot based on the provided dataset (43, 44, 45, 46, 47, 48), let's first calculate the quartiles.

  1. Minimum: The minimum value is 43.
  2. Maximum: The maximum value is 48.
  3. Median (Q2): Since there are 6 data points, the median is the average of the 3rd and 4th values: (45 + 46) / 2 = 45.5.
  4. Lower Quartile (Q1): This is the median of the first half of the data (43, 44, 45). The median of this set is 44.
  5. Upper Quartile (Q3): This is the median of the second half of the data (46, 47, 48). The median of this set is 47.

Now, summarizing the quartiles:

  • Minimum: 43
  • Q1: 44
  • Median (Q2): 45.5
  • Q3: 47
  • Maximum: 48

Box Plot Analysis

The box plot description states:

  • The first box extends from 45 to 45.5 (which only represents part of the data and does not correctly represent Q1 and Q3).
  • The second box extends from 45.5 to 46 (which again inaccurately represents the distribution).

Conclusions

  • The minimum value is correctly depicted as starting at 43.
  • The maximum value is correctly depicted at 48.
  • The first box should be from 44 to 45.5 (Q1 to median).
  • The second box should be from 45.5 to 47 (median to Q3).

Error Type

The box plot displays the wrong quartile values since Q1 and Q3 are incorrectly represented. Therefore, the correct response is:

The box plot displays the wrong quartile values.