Applied Quantitative Methods Group Assignment

HOLMES INSTITUTE
FACULTY OF
HIGHER EDUCATION
Trimester T1 2019
Unit Code HA1011
Unit Title Applied Quantitative Methods
Assessment Type Assessment 2
Assessment Title Group Assignment

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Attempt all the questions (8x2.5 = 20 Marks)
Question 1 of 8
HINT: We cover this in Lecture 1 (Summary Statistics and Graphs)
Data were collected on the number of passengers at each train station in Melbourne. The numbers
for the weekday peak time, 7am to 9:29am, are given below.
456 1189 410 318 648 2300 382 248 379 1240 2048 272
267 1134 733 262 682 906 338 1750 530 1584 3045 323
1311 1536 1606 982 878 169 583 548 429 658 344 2450
538 494 1946 268 435 862 866 579 1348 1022 1618 1021
401 1181 1178 637 2745 1000 2900 962 697 401 1442 1115
Tasks:
a. Construct a frequency distribution using 10 classes, stating the Frequency, Relative
Frequency, Cumulative Relative Frequency and Class Midpoint
Answer
Class Midpoint Frequency Cumulative
frequency
Relative
frequency
Cumulative relative
frequency
161-460 310.5 18 18 30.0% 30.0%
461-760 610.5 12 30 20.0% 50.0%
761-1060 910.5 9 39 15.0% 65.0%
1061-1360 1210.5 8 47 13.3% 78.3%
1361-1660 1510.5 5 52 8.3% 86.7%
1661-1960 1810.5 2 54 3.3% 90.0%
1961-2260 2110.5 1 55 1.7% 91.7%
2261-2560 2410.5 2 57 3.3% 95.0%
2561-2860 2710.5 1 58 1.7% 96.7%
2861-3160 3010.5 2 60 3.3% 100.0%
b. Using (a), construct a histogram. (You can draw it neatly by hand or use Excel)
Answer
HA1011 APPLIED QUANTITATIVE METHODS

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c. Based upon the raw data (NOT the Frequency Distribution), what is the mean, median and
mode? (Hint – first sort your data. This is usually much easier using Excel.)
Answer
Column1
Mean 976.5666667
Standard Error 90.58561006
Median 797.5
Mode 401
Standard Deviation 701.6731183
Sample Variance 492345.165
Kurtosis 1.19693607
Skewness 1.28094015
Range 2876
Minimum 169
Maximum 3045
Sum 58594
Count 60
Mean= 976.57
Mode=401
Median=797.5
Question 2 of 8
HINT: We cover this in Lecture 2 (Measures of Variability and Association)
You are the manager of the supermarket on the ground floor of Holmes Building. You are
wondering if there is a relation between the number of students attending class at Holmes Institute
each day, and the amount of chocolate bars sold. That is, do you sell more chocolate bars when
HA1011 APPLIED QUANTITATIVE METHODS

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there are a lot of Holmes students around, and less when Holmes is quiet? If there is a relationship,
you might want to keep less chocolate bars in stock when Holmes is closed over the upcoming
holiday. With the help of the campus manager, you have compiled the following list covering 7
weeks:
Weekly attendance Number of chocolate bars sold
472 6 916
413 5 884
503 7 223
612 8 158
399 6 014
538 7 209
455 6 214
Tasks:
a. Is above a population or a sample? Explain the difference.
This is a sample since it contains not all the elements. A population contains the entire
elements
b. Calculate the standard deviation of the weekly attendance. Show your workings. (Hint –
remember to use the correct formula based upon your answer in (a).)
x= 472+ 413+503+612+399+538+ 455
7 =484.57
stdev= √ ( xi−x )2
n−1
√ ( 472−484.58 )2+ ( 413−484.58 )2 + ( 503−484.58 )2 + ( 612−484.58 )2 + ( 399−484.58 )2 + ( 538−484.58 )2+ ( 455
6
¿ 74.0605
c. Calculate the Inter Quartile Range (IQR) of the chocolate bars sold. When is the IQR more
useful than the standard deviation? (Give an example based upon number of chocolate bars
sold.)
lower percentile=6114
upper percentile=6916
IQR=6916−6114=802
The interquartile range is more useful when data is skewed (not normally distributed)
d. Calculate the correlation coefficient. Using the problem we started with, interpret the
correlation coefficient. (Hint – you are the supermarket manager. What does the correlation
coefficient tell you? What would you do based upon this information?)
Weekly attendance Chocolate sales
Weekly attendance 1
Chocolate sales 0.967993 1
HA1011 APPLIED QUANTITATIVE METHODS