Use the image to answer the question.

Question

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 values.
The box plot displays the wrong 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.

Answer 1

To evaluate the error on the box plot, we first need to determine the correct quartiles, median, minimum, and maximum of the provided dataset: 43, 44, 45, 46, 47, 48.

1. Minimum: 43
2. Maximum: 48
3. Median: The median is the average of the two middle numbers (45 and 46) because there are 6 data points. So, \( \text{Median} = \frac{45 + 46}{2} = 45.5 \).
4. Lower Quartile (Q1): The first quartile is the median of the first half of the data (43, 44, 45), which is 44.
5. Upper Quartile (Q3): The third quartile is the median of the second half of the data (46, 47, 48), which is 47.

Now, let's compare these values with those represented in the box plot:

• The box plot shows two boxes from 45 to 45.5 and from 45.5 to 46, indicating incorrect quartiles.
• The minimum value displayed in the plot seems to be 43, which is correct, and the maximum at 48 is also correct.
• However, the median representation of 45.5 is correct, but the way it's depicted in the box plot doesn't align with the proper quartile values.

Given this analysis, the most accurate response is:

The box plot displays the wrong quartile values.