Question

he stem - and - leaf plot and some descriptive statistics of the grades, in percent, of a world history class are given below. stem - and - leaf display: grade n = 90 leaf unit = 1.0 5 | 00000011111111111222333333333334444444 5 | 555567777777888889999 6 | 0001122233344 6 | 68899 7 | 0111233 7 | 667 8 | 69 9 | 5 n q1 q3 90 53.211 63.223 key 2 | 3 = 23 how many of these grades are identified as outliers?

Explanation:

Step1: Calculate the inter - quartile range (IQR)

The formula for \(IQR = Q3 - Q1\). Given \(Q1 = 53.211\) and \(Q3 = 63.223\), then \(IQR=63.223 - 53.211=10.012\).

Step2: Determine the lower and upper bounds

The lower bound is \(Q1-1.5\times IQR\) and the upper bound is \(Q3 + 1.5\times IQR\).
For the lower bound: \(53.211-1.5\times10.012=53.211 - 15.018=38.193\).
For the upper bound: \(63.223+1.5\times10.012=63.223 + 15.018=78.241\).

Step3: Count the number of outliers

We check each data point from the stem - and - leaf plot.
The data points \(86\), \(89\), \(95\) are greater than \(78.241\).

Answer:

\(3\)