Download MATH 109 Sample Problem

MATH 109
Sample Problem
A group of freshmen in the Honors Program at WKU were asked to give the number of
hours they work per week at a job. The results were:
Hours
# Students
0
2
10
8
12
10
15
7
18
5
20
4
24
3
30
1
(a) Assuming that this group is the entire population under consideration, give the
correct notation for and the value (to three decimal places) of
(i) the mean: µ = 14.425
(ii) the standard deviation: ! " 5.787
(iii) Explain how the median is found
in this case and give its value.
There are 40 values in increasing order.
The median is the average of the 20th
and 21st value: (12 + 15)/2 = 13.5
(iv) Explain what the mode is in this case.
The mode is 12 hrs because it occurs
most often (10 times).
(v) Give the values of Q1 and Q3 and explain what they are.
Q1 = 11, it is the median of just the values below the actual median of 13.5
Q3 = 18, it is the median of just the values above the actual median of 13.5
(vi) Compute the percentage of these students whose number of hours is within one
standard deviation of average.
µ ± ! = 14. 425 ± 5.787
! 8.638 to 20.212 which contains measurements 10, 12, 15, 18, 20
There are
8 + 10 + 7 + 5 + 4 34
or 85% in this range.
=
40
40
(b) Assuming this group is only a random sample from a larger population, give the
correct notation for and the value (to three decimal places) of
(i) the sample mean
(ii) the sample deviation
x = 14. 425
S ! 5.861
(iii) Compute the 1.5 IQR bounds and then give the outliers.
The 1.5 IQR bounds are Q1 ! 1. 5(Q3 ! Q1 ) to Q3 + 1. 5(Q3 ! Q1 ) .
First, Q3 ! Q1 = 18 ! 11 = 7
Then the 1.5 IQR bounds are 11 ! 1.5 " 7 to 18 + 1. 5 ! 7 , or
0.5 hrs to 28.5 hrs
The outliers are the measurements outside this range, which are 0 hrs and 30 hrs.
(iv) Make a histogram with range [0, 35] and bins of length 5. Write the bin ranges in
interval form and give the frequencies in each bin.
WINDOW
STAT PLOT
[0, 5) has 2 values
Graph
[10, 15) has 18 values
[20, 25) has 7 values
Trace
[15, 20) has 12 values
[30, 35) has 1 value
(v) In this case, what is an appropriate larger population that this sample could
represent?
The sample could represent all freshmen in the Honors Program at WKU.