Question

interpreting a box plot
between which two values would 50% of the data lie? choose three correct answers.
45 and 60
40 and 50
15 and 40
15 and 45
45 and 50

Explanation:

Step1: Recall box - plot properties

In a box - plot, the inter - quartile range (IQR) (the box part) contains 50% of the data. Also, the lower half (from the minimum to the median) can contain 50% of the data (if the data is symmetric, but in general, the part from the minimum to the median and from the median to the maximum each can be considered in terms of data spread).

Step2: Analyze each option

• Option 1: 45 and 60

The box - plot has the box (IQR) and the whiskers. If we consider the upper half of the data (from the median to the maximum), assume the median is 45 (the middle line of the box). If the upper quartile is 50 and the maximum is 60, this is not the IQR.

• Option 2: 40 and 50

The box of the box - plot (IQR) is from the lower quartile \(Q_1\) to the upper quartile \(Q_3\). If \(Q_1 = 40\) and \(Q_3=50\), the IQR (\(Q_3 - Q_1\)) contains 50% of the data.

• Option 3: 15 and 40

If the minimum is 15 and \(Q_1 = 40\), the part from the minimum to \(Q_1\) (the lower half of the data before the box) can contain 50% of the data (since the box (IQR) contains 50% and the two halves (below \(Q_1\) and above \(Q_3\)) can each be considered as 25% + 25% in a non - symmetric case. But if we assume the data is split such that from the minimum (15) to \(Q_1\) (40) contains 50% of the data (for example, if the median is 45 and \(Q_3 = 50\), the data below the median can be further split. If the lower half (from 15 to 45) is considered, but if \(Q_1 = 40\), from 15 to 40 (lower quartile) can be 50% in some data distributions.

• Option 4: 15 and 45

If the median is 45, the part from the minimum (15) to the median (45) contains 50% of the data (by the definition of the median: 50% of the data is below the median and 50% is above the median).

• Option 5: 45 and 50

This is a part of the box (if \(Q_1 = 40\), \(Q_3 = 50\) and median = 45), but it only contains 25% of the data (from the median to \(Q_3\)).

Answer:

15 and 40, 15 and 45, 40 and 50