HA1011 Group Assignment - Summary Statistics, Measures of Variability and Association, Linear Regression, Probability

HOLMES INSTITUTE
FACULTY OF HIGHER EDUCATION
HA1011 Group Assignment
Due End of Week 10
WORTH 20%
(Maximum 5 students in the group)
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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 410 318 648 399 382 248 379 1240 2268 272
267 1113 733 262 682 906 338 1750 530 1584 2985 323
1311 1632 1606 982 878 169 583 548 429 658 344 2630
538 494 1946 268 435 862 866 579 1359 1022 1618 1021
401 1181 1178 637 2830 1000 2958 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
Interval
Mid-point Frequency Relative
Frequency
Cumulative Relative
Frequency
100-400 250 13 21.67% 21.67%
401-700 550 17 28.33% 50.00%
701-1000 850 8 13.33% 63.33%
1001-1300 1150 8 13.33% 76.67%
1301-1600 1450 4 6.67% 83.33%
1601-1900 1750 4 6.67% 90.00%
1901-2100 2050 1 1.67% 91.67%
2101-2400 2350 1 1.67% 93.33%
2401-2700 2650 1 1.67% 95.00%
2701-3000 2950 3 5.00% 100.00%
b. Using (a), construct a histogram. (You can draw it neatly by hand or use Excel)
Answer
2

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
Number of passengers
Mean 954.37
Median 715
Mode 401
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 below Holmes. You are
wondering if there is a relation between the number of students attending class at Holmes
each day, and the amount of chocolate bars sold. That is, do you sell more chocolate bars
when 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:
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Weekly attendance Number of chocolate bars sold
472 6916
413 5884
503 7223
612 8158
399 6014
538 7209
455 6214
Tasks:
a. Is above a population or a sample? Explain the difference.
Answer
This is a sample. This is because the data is just for a selected number of weeks.
Population would have required considering all the dataset since Holmes probably
started.
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).)
Answer
x= 472+ 413+503+612+399+538+ 455
7 = 3392
7 =484.5714
SD= √ ∑
i=1
n
( xi−x )2
n−1 = √ ( 472−484.57 )2+ ( 413−484.57 )2 +...+ ( 538−484.57 )2 + ( 455−484.57 )2
30−1 = √ 32909.71
7−1 =
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.)
Answer
IQR=Q3−Q1
Q3=7216
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