Study Master, Chapter 2
McGraw-Hill
Ryerson Mathematics of Data Management, pp. 151–153
1. The data in the table at the right represent the
shoe lengths, in centimetres, of 36 students.
|
a) Construct an appropriate graph for this set
of data, using intervals. b) If these data represented shoe sizes
instead of lengths, what type of graph should be used? Explain. c) What percent of the shoe
lengths were between 27 cm and 30 cm? |
28.3 |
24.1 |
20.8 |
32.6 |
30.2 |
18.2 |
|
22.3 |
26.0 |
25.5 |
36.1 |
25.4 |
22.1 |
|
|
26.9 |
30.2 |
32.7 |
29.3 |
28.6 |
30.1 |
|
|
35.7 |
20.1 |
27.4 |
32.1 |
34.0 |
31.8 |
|
|
30.1 |
29.7 |
28.6 |
31.2 |
25.3 |
27.0 |
|
|
24.1 |
28.6 |
27.5 |
28.6 |
29.2 |
30.5 |
d) What percent of the shoe
lengths were at least 33 cm?
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2. The UV index is a measure
of the intensity of the sun’s ultraviolet rays in the sun-burning spectrum.
The UV index is dependent upon such conditions as latitude, altitude,
reflection, and cloud cover. The published UV Index is the maximum value
expected at solar |
UV Index |
Category |
|
Over 9 |
Extreme |
|
|
7 to 9 |
High |
|
|
4 to 7 |
Moderate |
|
|
0 to 4 |
Low |
The following graph shows the UV Index for a
particular city during July.
a) By approximately how many points did the UV
index jump between July 8 and July 12?
b) What type of graph is used here?
c) Why is this index not a cumulative index
relative to a specific year?
d) Explain the fluctuation in UV levels.
3. A national cereal company is planning to introduce a new children’s breakfast cereal and wants to survey people about their reaction to the proposed brand name.
a) Describe how you would design each of the following samples.
i) A systematic sample
Study Master,
Chapter 2 [Continued]
ii) A stratified sample
iii) A convenience sample
b) What are the advantages and disadvantages of sampling only children?
4. A
consumer advocacy association asks its members to submit their responses to its
annual survey on automobile repairs, (including type, cost and number of
repairs), dealer satisfaction, and willingness to purchase from that
manufacturer again.
a) Describe the type of bias present in this
survey.
b) How could bias be reduced or eliminated?
5. Rewrite
the following survey question to eliminate the measurement bias: “In light of
the poor showing at the box office, do you think this movie deserves to be
nominated for a Genie Award?”
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6. A waiter recorded his tips from his 50 customers one day. He recorded them as grouped data as shown in the table at the right. Border values are included into the upper interval. a) Calculate the mean, median and mode of his tips. b) Which measure best describes these data? c) How do outliers affect the measures? d) Calculate the population standard deviation. e) Calculate the inter-quartile range. f) For the entire staff, mean = $8.19, median = $7.00, mode = $5.00, |
|
Frequency |
|
0–2 |
4 |
|
|
2–4 |
5 |
|
|
4–6 |
20 |
|
|
6–8 |
4 |
|
|
8–10 |
0 |
|
|
10–12 |
8 |
|
|
12–14 |
2 |
|
|
14–16 |
5 |
|
|
16–18 |
0 |
|
|
18-20 |
2 |
standard deviation = $4.213, IQ range = $6
How do this waiter’s measures compare with those from the entire staff?
g) What is the z-score of a tip of $15? What does that z-score mean?
h) What might explain the peaks in the intervals 4–6, 10–12, and 14–16?
Study Guide
For help with a specific question or type of question, review the examples specified below.
Question
|
Section |
Refer to: |
|
1 |
2.1 |
Example 1 |
|
2 |
2.2 |
Examples 1, 2 |
|
3 a) |
2.3 |
Example 2 |
|
3 b) |
2.3 |
Example 3 |
|
3 c) |
2.3 |
Other Sampling Techniques |
|
4 |
2.4 |
Examples 1, 2 |
|
5 |
2.4 |
Example 3 |
|
6 a), b), c), h) |
2.5 |
Examples 1, 4 |
|
6 d) |
2.6 |
Example 1 |
|
6 e) |
2.6 |
Example 3 |
|
6 f) |
2.5 |
Example 2 |
|
6 g) |
2.6 |
Example 6 |