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4 votes
Which box plot represents the data above?

W.
X.

Y.
Z.

A.
Z
B.
W
C.
X
D.
Y

User Maxbester
by
4.3k points

1 Answer

6 votes

Final answer:

Box plots provide a visual summary of data distribution, showing critical values like the minimum, Q1, median, Q3, and maximum. The shape indicates spread and skewness, and outliers are defined relative to the interquartile range (IQR). Accurate construction and analysis of box plots facilitate data interpretation and comparisons.

Step-by-step explanation:

Box plots, also known as box-and-whisker plots, are a graphical representation of data that summarize the distribution of a dataset. They are constructed using five key data points: the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.

The shape of a box plot can tell us a lot about the distribution. For instance, a long left whisker indicates that the lower half of the data is spread out more than the upper half. When analyzing box plots, we look at the range, which is the difference between the maximum and minimum values, as well as the interquartile range (IQR), which is the range of the middle 50 per cent of the data contained within the box.

When deciding whether a statement about a box plot is true or false, we must consider the quartiles and median represented. For example, if a statement says that 25 per cent of the data are at most five, this would be true if the value at Q1 is five. A statement about the amount of data between certain ranges must consider both the range and distribution of the data within the box and whiskers.

When constructing a box plot, accuracy is crucial. You must use a ruler to scale accurately and draw straight edges. You should also consider whether there are any potential outliers, which are typically defined as values that are less than Q1 - 1.5(IQR) or more than Q3 + 1.5(IQR).

User Justinpinili
by
5.1k points