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MDM4U1 Assignment 5- One Variable Statistics | Complete Solution
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MDM4U1            Assignment 5- One Variable Statistics

Name:______________________ KU:   /22   APP:       /12     COMM:   /7  TI:      /10

Knowledge
1. Eighteen executives reported the following number of telephone calls made during a randomly
selected week.
28    8    13    30    51    19
19    12    17    49    10    14
8    21    35    28    36    12

Find the following. Show all your work clearly.
(a) Range                                                                [1]

(b) Q1
[2]

(c) Q2
[2]

(d) Mode
[1]

(e) D9

(f) Q3

(g) The interquartile range

(h) The standard deviation for this sample

(i) Variance for this sample

(j) Coefficient of variation

(k) Interpercentile range between   P20  and  P80.

(l) Draw a box and whisker plot for this data.

2. The mean of 4 numbers is 12 and the mean of 3 different numbers is 21. What is the mean of
the 7 numbers together? Produce an algebraic solution. Guess and check is unacceptable [2].

Application

3. Delivery time for a sample population of 80 pizzas are as follows:

time
(minutes)    frequency
0.5 to 10.5    5
10.5 to 20.5    36
20.5 to 30.5    24
30.5 to 40.5    12
40.5 to 50.5    3

(a) The mean delivery time [2]               (b) The standard deviation of the delivery times [3]

(c) Coefficient of variation for this sample [2]

4.  An academic award is to be granted to the student with the highest overall score in four weighted
categories. Here are the scores for the three finalists:                             [5]

Criterion    Weighting Factor    Carl    Fred    Sandra
Academic Achievement    3    4    3    5
Extra-Curricular Activities    2    4    4    4
Community Service    2    2    5    3
Interview    1    5    5    4

Calculate the weighted-mean score for each student. Who should win the award?

Communication

5.    Suppose that teachers receive a 5% raise each year.  The amount of the raise will vary from \$1500 to \$3000, depending on recent salary.  How would a 5% across-the-board raise affect the interquartile range, the standard deviation, and the variance? Provide some mathematical justification to show by what percentage each would increase/decrease?    [5]

6.    In a group of 1200 students, Raymond received a score of 86% at the Waterloo Senior Math Contest.
This puts him in the 92nd percentile.  Explain what this means.          [2]

Part D: Thinking/Inquiry

7.    Sarina is in Mr. Dadar’s Calculus class. She has written three evaluations so far (one test and two quests).  Category weightings are as follows:

K/U    APP    Inquiry    Communication
25%    20%    15%    10%
Each quest has a weight factor of 2 in each category that is being assessed and a test has a weight factor of 3 for each category. She has received the following marks.

Quest 1    K/U:   5/8    APP:  7/10
Test 1    K/U:  12/13    APP:   19/24    Inquiry: 7/11    Com.   7/8
Quest 2        APP: 7 /11        Com.   8/8

What is her current mark in the course? Approximate your final answer to one decimal place.  [7]

8.   Calculate P30 for question #3.  [3]

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MDM4U1 Assignment 5- One Variable Statistics | Complete Solution
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• Submitted On 22 May, 2017 11:57:44
Solution posted by
Q2 = 2(18+1)/4 = 9.5th data = 19+0.5(19-19) = 19 (d) Mode [1] There are 4 modes 8, 12, 19 and 28 (e) D9 ...
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