Question

3. Below are the final exam scores of 25 introductory statistics students.
   42, 53, 63, 76, 76, 78, 80, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 91, 92, 94, 95, 95, 96, 96, 97

   Create a box plot of the distribution of these scores.Please indicate the values the boundaries and the middle line of the box represent respectively, use the 1.5 IQR rule to identify outlier(s) if any, and show how you determine the values the two whiskers extend to.

Answer 1

n = 25

Therefore Median = {(n+1)/2}th value in the arrange data set

So here median = 13th value = 88

Median = 88

Q1 = middle value of the data before Median in the arrange data set

that is Median of the first 12 values = average of 6th and 7th value = (78 + 80)/2 = 79

So Q1 = 79

Q3 = middle value of the data after the Median in the arrange data set

that is Median of the last 12 values = average of 19th and 20th value = (92 + 94)/2 = 93

So Q3 = 93

Minimum = 42

Maximum = 97

The formula of IQR is as follows:

IQR = Q3 - Q1 = 93 - 79 = 14

We now multiply by 1.5 and have 1.5 x 14 = 21.

21 than the first quartile is 79 – 21 = 58 . Two data values are less than 58 as 42 and 53 which are outliers.

21 more than the third quartile is 93 + 21  = 114. No data is greater than this.

So the box plot of the distribution of these scores are as follows: