Question

Solve the following:

3. (6 pts.) Eighteen faculty members in a college math department range in age from 32 to 75. The ages are as given below: 32 34 38 39 39 49 53 54 57 58 40 43 45 46 59 59 68 75 (a) Construct a stem and leaf plot of the data. (b) Determine the quartiles Q1, Q2, Q3. (c) Does the data contain any outliers? Compute the inner fences, outer fences and identify mild and extreme outliers, if any. Draw a box plot indicating outliers, if any.

Answer 1

a) The stem and leaf plot is as:

Stem Leaf 3 24899 4 03569 5 34 7 8 9 9

Where ,3| 2= 32

b) The Five-point summary for the given sample {32, 34, 38, 39, 39, 40, 43, 45, 46, 49, 53, 54, 57, 58, 59, 59, 68, 75}
is :

Minimum=32

Q1= Median of the first half = 39

Q2= median =47.5

Q3= median of the 2nd half data = 58

Maximum=75

c) To find any outlier we need to find the fences for outliers as:

Lower fence= Q1- 1.5 *IQR, where IQR is the interquartile range = Q3-Q1= 58-39=19 so, lower fence

=39-1.5*19

=10.5

Upper limit= Q3+1.5*IQR

=58+1.5*19

=86.5

Since no value lies outside the fence limit hence there is none outliers.

The Box plot is plotted using Excel tool as: