Advanced Math 45S
Unit 2: Statistics Assignment
Statistics Assignments
Assignment #1
1. Explain whether each of the following constitutes a population or a sample.
a. Number of personal fouls committed by all NBA players during the
2011-2012 season
b. Yield of potatoes per acre for 10 pieces of land
c. Weekly salaries of all employees in a company
d. Cattle owned by 100 farmers in Iowa
e. Number of computers sold during the past week at all computers in
Winnipeg.
2. Which sampling method would you use to select a sample from:
a. A high school
b. Batteries on a production line
c. Homeless people of Winnipeg
3. A high school has 350 students in grades 9 to 12, with 100 in grade 9, 75 in
grade 10, 85 in grade 11 and 90 in grade 12. A committee of 20 students is
needed. Describe how a selection could be made so that it closely resembles
the population
Assignment #2
1. Find the mean, median, and mode for each set of data
a. 4,6,9,12,5
b. 7,13,4,7
c. 10,3,8,15
d. 9,9,9,9,8
e. 300,24,40,50,60
f. 23,23,12,12
2. In a basketball game between Kennedy High School and Lincoln High School, the
Lincoln players’ individual points were 23, 4, 6, 11, 4, 7, 8, 12, 3, and 5. Find the mean,
median, and mode of the individual points.
3. Olivia swims the 50-yard freestyle for the Mud Dogs swim team. Her times in the last
six meets were 26.89 seconds, 26.27 seconds, 25.18 seconds, 25.63 seconds, 27.16
seconds, and 27.18 seconds. Find the mean and median of her swimming times.
Advanced Math 45S
Unit 2: Statistics Assignment
4. Find the mean, median and mode from the following frequency tables
a)
5. The following are the salaries of 5 employees in a small business:
Mr A: $22,500
Mr D: $22,500
Mr B: $17,900
Mr E: $85,000
Mr C: $21,900
a) Find the mean, median and mode of their salaries.
b) Which does NOT give a fair “average”? Explain why.
6. A farmer has 32 cattle to sell. The weights in kg are:54
81
85
91
154
81
86
92
320
82
86
93
370
82
87
94
375
83
87
96
376
84
88
150
380
84
89
152
381
85
91
153
390
(Total weight = 5028kg)
On the telephone to a potential buyer the farner describes the cattle and says the
‘average’ weight is ‘over 157kg’.
a) Find the mean weight and the median weight.
b) Which average has the farmer used to describe his animals? Does this average
describe the cattle fairly?
Assignment #3
1. The junior high basketball team played ten games. Find the standard deviation for
the number of baskets scored by the team for the ten games:
8, 4, 6, 6, 7, 7, 9, 4, 8, 5.
Advanced Math 45S
Unit 2: Statistics Assignment
2. Find the standard deviation for the following test scores. Use the chart below to
record the steps.
85, 100, 92, 96, 87, 94
3. A company that provides a vehicle for each of their eight employees, monitors the
amount of gasoline used by each employee. The following list is the amount of
gasoline, in litres, used by the employees. What is the variance and standard
deviation.
42, 21, 38, 42, 63, 42, 26, 30
4. McDonald’s monitors the amount of time, in minutes, that a customers waits for their
order while going through the drive-thru. The boss tells the staff that their serving
time is good if the standard deviation is under 4 minutes. How did they do if the
following times were recorded? 5, 3, 2.5, 8, 15, 4, 4.5, 6.5, 2, 9
5. The following is a random selection of marks taken from two Algebra 2 classes. Which
class has a lower variation of scores?
Section 1: 42, 56, 60, 62, 67, 90
Section
2: 45, 58, 61, 75, 87, 93
6. A production engineer can use either of two methods to make car batteries. He
takes a random sample of 8 batteries made by each method and measures the
lifetime of each bettery. The lifetimes in months are given below.
Method A
Method B
21
23
24
27
22
20
23
22
25
26
23
20
26
27
20
19
Find the mean and standard deviation of each sample. Which method would you
recommend the engineer to use in the future? Give your reason.
7. Calculate the standard deviation of the following frequency tables
a.
x
3
4
5
6
7
8
Freq
9
3
15
21
28
3
2
1
x
4.9
5.2
6.3
7.5
8.1
8.6
9.0
Freq
1
5
6
9
5
2
1
b
Advanced Math 45S
Unit 2: Statistics Assignment
Assignment 4
1. Determine the percentile rank for the students who scored 72 in a chemistry test if
the class results are as follows:
18
27
38
40
42
45
45
48
52
53
56
58
59
61
64
67
68
70
72
72
73
75
82
83
83
83
85
85
89
90
90
97
2. Xavier scored 82% on her biology exam. There were 199 other students who
wrote the same exam. No one received the same score as her but 135 students
received a lower score. What is her percentile ranking?
3. A student scored 35% on a recent Math test. However the student’s perecentile
rank was 82. What can you conclude about the success rate of most other
students? What could cause test results like this?
4. The following statistics are available on the family income for a community that
has 2200 families.
P25 = $15,500
P50 = $28,475
P75 = $42,750
P85 = $64, 250
a) What percent of the families earn $28,475 or less? How many families earn
$28,475 or less?
b) What percent of families earn more than $64,250?
c) What percent of families earn $42,750 or less?
d) What percent of families earn more than $15,500?
e) What percent of families earn more than $15,500 but less than or equal to
$64,250? How many families would this be?
f) What is the median family income for this community?