Question

charles wants to analyze his last 9 math test scores with a box - plot to see how spread apart they are. construct a box plot to examine the measures of variability. charless scores: 80, 84, 86, 87, 90, 91, 92, 94, 100. use the box plot to answer the questions. what is the range of charless scores? what is the median of charless scores? what is the iqr of charless scores?

Explanation:

Step1: Recall range formula

The range is the difference between the maximum and minimum values. Given scores are 80, 84, 86, 87, 90, 91, 92, 94, 100. The maximum value is 100 and the minimum is 80. So, Range = 100 - 80.

Step2: Calculate range

Range = 20.

Step3: Recall median concept

For a set of 9 (odd - numbered) data points, the median is the middle - numbered value. Arranging the data in ascending order: 80, 84, 86, 87, 90, 91, 92, 94, 100. The 5th value is the median. So, Median = 90.

Step4: Recall IQR concept

The inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). For a set of 9 data points, the first quartile is the value at the position $\frac{n + 1}{4}= \frac{9+ 1}{4}=2.5$, so $Q_1$ is the average of the 2nd and 3rd ordered values. $Q_1=\frac{84 + 86}{2}=85$. The third quartile is the value at the position $3\times\frac{n + 1}{4}=3\times\frac{9 + 1}{4}=7.5$, so $Q_3$ is the average of the 7th and 8th ordered values. $Q_3=\frac{92+94}{2}=93$. Then, IQR=$Q_3 - Q_1=93 - 85$.

Step5: Calculate IQR

IQR = 8.

Answer:

What is the range of Charles's scores? 20
What is the median of Charles's scores? 90
What is the IQR of Charles's scores? 8