Question

read the prompt/s below and answer accordingly. validate with desmos if necessary.

1. which of the following data sets is represented by the box plot above?

a. 50, 51, 52, 55, 58, 60, 65, 58, 58
b. 50, 51, 52, 55, 58
c. 50, 56, 50, 56, 57, 55, 58, 50, 59, 55, 50, 50

1. what is the iqr of the above? _______________

Explanation:

Sub - Question 1

Step 1: Analyze the box - plot

From the box - plot, the minimum value is 50, the maximum value is 60. Let's analyze each option:

• Option A: The data set is 50, 51, 52, 55, 58, 60, 65, 58, 58. Here, the maximum value is 65, but from the box - plot, the maximum value is 60. So, option A is incorrect.
• Option B: The data set is 50, 51, 52, 55, 58. The number of data points is 5, and the box - plot seems to represent a data set with more data points (since a box - plot is usually for a relatively larger data set). Also, the maximum value in the box - plot is 60, but in this data set, the maximum is 58. So, option B is incorrect.
• Option C: The data set is 50, 56, 50, 56, 57, 55, 58, 50, 59, 55, 50, 50. The minimum value is 50, the maximum value is 59 (wait, no, 59 is less than 60? Wait, maybe I made a mistake. Wait, let's re - check. Wait, the box - plot's whisker on the right ends at 60? Wait, the dot on the right is at 60. Wait, in option C, the data points are 50, 50, 50, 50, 50, 55, 55, 56, 56, 57, 58, 59. Wait, no, when we sort option C: 50, 50, 50, 50, 50, 55, 55, 56, 56, 57, 58, 59. The maximum is 59, but the box - plot has a dot at 60. Wait, maybe there is a mistake in my initial analysis. Wait, maybe the box - plot's maximum is 60, but in option C, if we consider that maybe a data point is 60? Wait, no, the data set in option C is 50, 56, 50, 56, 57, 55, 58, 50, 59, 55, 50, 50. When sorted: 50, 50, 50, 50, 50, 55, 55, 56, 56, 57, 58, 59. The maximum is 59. But the box - plot has a dot at 60. Wait, maybe the first option's maximum is 65, which is wrong. Option B has only 5 data points. Option C, even though the maximum is 59, maybe it's a typo or my mis - reading of the box - plot. Wait, maybe the box - plot's right dot is at 60, but the data set in option C is the only one with minimum 50 and a reasonable spread. Option A has a maximum of 65, which is outside the box - plot's range. Option B has too few data points and wrong maximum. So, option C is the best among the three.

Step 2: Confirm the data set

After eliminating option A (due to max = 65) and option B (too few data points, wrong max), option C is the correct one.

Step 1: Recall the formula for IQR

The inter - quartile range (IQR) is calculated as \(IQR = Q_3-Q_1\), where \(Q_1\) is the first quartile and \(Q_3\) is the third quartile.

Step 2: Determine \(Q_1\) and \(Q_3\) from the box - plot

From the box - plot, the lower quartile (\(Q_1\)) is at 54 and the upper quartile (\(Q_3\)) is at 57 (assuming the box starts at 54 and ends at 57? Wait, looking at the number line: the box is between 54 and 57? Wait, the box has two parts, but the left end of the box is at 54 and the right end of the box is at 57? Wait, the number line has marks at 50, 52, 54, 56, 58, 60. Let's assume that the first quartile (\(Q_1\)) is 54 and the third quartile (\(Q_3\)) is 57.

Step 3: Calculate the IQR

Using the formula \(IQR=Q_3 - Q_1\), we substitute \(Q_3 = 57\) and \(Q_1 = 54\). Then \(IQR=57 - 54=3\).

Answer:

C. 50, 56, 50, 56, 57, 55, 58, 50, 59, 55, 50, 50

Sub - Question 2