ADACC - Chapter 12

This document provides information on ADACC - Chapter 12, including short answer questions, frequency table, mean, median, mode, range, standard deviation, and inter-quartile range.

ADACC – Chapter 12
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ADACC – Chapter 12
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ADACC – Chapter 12
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ADACC – Chapter 12
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ADACC – Chapter 12
Short Answer Question 1:
Listed below are the earnings of a group of accounting graduates in their first year at work. All amounts are in thousands of
dollars:
29.5, 30.2, 31.5, 24.3, 40.5, 37.3, 27.4, 35.2, 32.1, 34.6
33.4, 37.4, 26.8, 34.0, 34.7, 39.0, 40.5, 38.0, 29.6, 30.4
41.7, 35.4, 33.7, 38.6, 36.5, 32.2, 37.5, 28.4, 37.1, 35.8
For the same data set:
a) Prepare a frequency table using the class intervals given.
b) Calculate the mean, the median and the mode. Show your workings
c) Calculate the range and the standard deviation. Use MS Excel to calculate the Standard Deviation.
d) For the same data set calculate the inter-quartile range. Show your workings.
(a)
Earnings
$000’s Frequency % Cumulative
Frequency Cumulative %
24 - < 27
27 - <30
30 - <33
33 - < 36
36 - <39
39 - <42

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(a)Frequency table
Table 1Cumulative frequency and frequency table
Row Labels Frequency Percentage
Cumulative
frequency
Cumulative
percentage
24.3-27.3 2 7% 2 7%
27.3-30.3 4 14% 6 21%
30.3-33.3 4 14% 10 34%
33.3-36.3 8 28% 18 62%
36.3-39.3 8 28% 26 90%
39.3-42.3 3 10% 29 100%
Grand Total 29 100%
It is the one of the main statistical tool that is used to analyse the dataset. It can be
observed that in the frequency table multiple classifications are made and frequency or
number of observations in these groups are demonstrated by the frequency tables. In the
above table percentage column is given which is indicating group that have higher share in
the dataset. It can be seen from the table that group 33.3 to 36.3 and 36.3 to 39.3 have
largest share in the dataset up to 28% individually. Chart of the frequency distribution is
given below.
(b) Mean, median and mode

ADACC – Chapter 12
Table 2Mean calculation
Row
Labels Frequency Mid-point Midpoint*frequency
24.3-27.3 2 25.8 51.6
27.3-30.3 4 28.8 115.2
30.3-33.3 4 31.8 127.2
33.3-36.3 8 34.8 278.4
36.3-39.3 8 37.8 302.4
39.3-42.3 3 40.8 122.4
Total 997.2
Mean 33.24
Interpretation
It is the one of the most important tool that is used to evaluate a variable in terms of
average performance it gives (Ho and Yu, 2015). In table given above it can be observed that mean
value is 33.24 which means that on an average basis sample unit have earning of $33.24. Those
who receive earning above this can be considered in category of high income people and those
who earn below average can be considered as low-income earners. Thus, it can be said that there is
huge significance of the mean as a tool because it reflects the broad picture of the variable.
Median calculation
Table 3Median calculation
Row Labels Frequency
24.3-27.3 2
27.3-30.3 4
30.3-33.3 4
33.3-36.3 8
36.3-39.3 8
39.3-42.3 3
Grand
Total 30
Median = (N+1)/2

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Mode is another most important statistical tool that is used to analyse data by the business firms. Mode reflect
value that is repeated often in the dataset. By considering mode value one can identify pattern in which variable
is moving in the particular time period (Goos and Meintrup, 2015). On basis of results prediction can be made
about the future movement of the variable. Thus, it can be said that there is significant importance of the mode
as a statistical tool for the firms and experts especially stock market analysts. In present case mode value is 36.3
which indicate that there are large number of people who earn $36.3.
( e) Range
Table 5Calculation of range
MAX 41.7
MIN 24.3
Range 17.4
STDEV 4.41
Range is another simple statistical approach which reflect the difference between maximum and minimum
value of the variable (Pyrczak, 2016). In the table given above it can be seen that maximum value of the
variable is 41.7 and minimum value of the variable is 24.3. Thus, difference between both is 17.4. Thus, it
can be said that difference between maximum and minimum value is moderate. It can be broadly interpreted
that there is medium difference between maximum and minimum earning in respect to sample units and
there is not a situation where few one is earning higher amount and some are earning low amount.
Standard deviation is the one of the most important tool that is used to identify extent to which
variable values are deviating from the mean value (LaFlair, Egbert. and Plonsky,, 2015). In case standard
deviation is high it can be said that variable values are deviating at fast pace from the mean value. On other
hand, if standard deviation is low then in that case it can be said that most of values are nearby to mean
value. In above table it can be seen that value of standard deviation is 4.41 which means that variables value
is not deviating at fast pace and is nearby to mean value. This is also evident from the medium range value
which indicate that within small range most of values are. Hence, in such kind of situation definitely
standard deviation value will be low.
(D) Interquartile range
Q1 = (N+1)/4
= (30+1)/4

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Short Answer Question 2:
a) When is it more appropriate to use the median as a measure of central tendency than the mean?
b) List two advantages of using the mean as a measure of central tendency.
(a)Appropriateness of median then mean as measure of central tendency
There is no best measure of central tendency. It depends on the data type that which of
measure of central tendency is assumed appropriate for the data analysis process. Median is
used as measurement of central tendency in case distribution is strongly skewed. In case
data is of ordinal type median is preferred over mean (Young and Wessnitzer, 2016).
However, if analyst want then in that case it can also use mode instead of median in the
data analysis process.
(b) Advantage of using mean as a measure of central tendency
One of the main advantage of using mean as a measure of central tendency is that it
indicates overall performance of the variable most of times. Thus, one can easily identify
behaviour of the variable and accordingly make decision. Other main benefit of using
average is that if it used along with standard deviation to analyse dataset one easily
identifies value around which most of data points lie.

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Short Answer Question 3:
In a pet store, there are 6 puppies, 9 kittens, 4 gerbils, and 7 parakeets. If a pet is chosen at random, what is the probability
of getting a puppy or a parakeet? Show your workings
Probability of Puppy = 6/26 = 3/13 = 23%
Probability of Parakeet = 7/26= 0.26 = 26%
Probability of get Puppy is 23% and same of getting Parakeet is 26%. Hence, it can be said
that probability is same in case of both Puppy and Parakeet.

ADACC – Chapter 12
Short Answer Question 4:
Assume 20% of males and 15% of females are left-handed, and that males and females each form 50% of the population. A
student observing left-handedness selects a left-handed person at random. What is the probability that the person selected
is:
a) Male?
b) Female?
Show your workings.
Let Total number of population be 100000
left handed male will be 20% of total = 20000
Left handed female will be 15% of the total = 15000
Probability of male= 2000/100000=0.2

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Short Answer Question 5:
A survey is to be taken by Oz University to discover student opinions on the provision of cafeteria facilities. Remember that
Oz University is a multi-campus institution, and that full and part-time students must be catered for.
a) Briefly outline a random sampling method which could be used to select a sample of 100 students for questioning.
b) State one main advantage and one disadvantage of the sample you devised in a) above.
(a)Sampling method
Simple random sampling method refers to the process where randomly sample units
are selected from the population. Lottery method can be used and under this randomly any
chit can be picked from the bowl and one can be selected as sample unit for research
purpose (Zhou and et.al., 2016). In context of University few student’s names can be
written on chit or from register name of the students can be evoked and by doing so from
multiple classes varied students can be picked randomly and from them data can be
collected and analysed further.
(b) Merit and demerit of the sampling approach
Main merit of the sampling approach is that without any biasness sample units will be
picked from the University (Verhagen and et.al., 2016). Major demerit of the sampling
method is that students can be picked as sample units that are not prudent to answer asked
questions. In that case wrong answers can be obtained from the sample units which is not
good from research point of view.

ADACC – Chapter 12
Short Answer Question 6:
A movie fan calculated that the mean running time of horror films made in the 1980’s was 90 minutes with a standard
deviation of eight minutes. Given that 7,250 horror films were made in the 1980’s how many would you expect to run for:
a) Between 66 and 114 minutes?
b) Between 74 and 106 minutes?
(a)
0.997×7250≈72280.997×7250≈7228 movies
(b)
0.954×7250≈69170.954×7250≈6917 movies

ADACC – Chapter 12
Short Answer Question 7:
The internal auditors for Accurate Accounting Systems carried out a random check of 30 employees for errors. The
investigation provided the following information:
Number of employees 0 1 2 3 4 5 6
Number of errors 2 4 5 7 6 4 2
Draw an appropriate cumulative frequency curve (histogram).

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Table 6Cumulative frequency table
Row Labels
Sum of Number of
employees
Cumulative
frequency
2 6 6
4 6 12
5 2 14
6 4 18
7 3 21
Grand
Total 21
1 2 3 4 5
0
5
10
15
20
25
6
12
14
18
21
Cumulative frequency
Cumulative frequency
Figure 1Cumulative frequency table

ADACC – Chapter 12
In case of number of errors, it can be observed that highest frequency is in case of 2 and 4
which means that majority of respondents are making error in number of 2 and 4. With
increase in error number, frequency of number of employees decline. This is evident from
the cumulative frequency graph where rate of growth of frequency is high in case of 1 and
2 then slightly this growth decline in case of 3rd 4th and 5th.

ADACC – Chapter 12
Short Answer Question 8:
Suppose a survey of 70 people produced the following results:
19 ate eggs for breakfast; 18 ate meat; 50 ate toast; 12 ate eggs and meat; 10 ate meat and toast; 13 ate eggs and toast;
and nine ate all three.
Illustrate using Venn diagram theory:
a) How many ate none of the three?
b) How many ate toast, but neither eggs nor meat?
c) How may ate eggs and meat but not toast?
d) What is the probability that a person ate meat only?
e) What is the probability that a person ate none of the three?
a) The number that ate none of the three = 70−70− (sum of above seven
values) =70−61=9=70−61=9.
b) The number that ate toast but neither eggs or meat =36=36.
c) The number that ate eggs and meat but not toast =3=3.
d) Probability that a person only ate meat =5/70=1/14=5/70=1/14.
e) Probability that a person ate none of the three =9/70=9/70.

ADACC – Chapter 12
Case Study Question:
Gerry’s Business Data for Year ending June 201X
Driver Data
Age Numbe
r
Ave
Annual
Wage
$000’s
Ave.
kms./
Driver /
Year
Total $
Fines for
Group
Gym
Membershi
p
Ave.
Sick
Days /
Year /
Driver
Ave
Turnove
r %
21-30 6 43.5 141,000 10,560 5 7 9.3
31-40 27 46.2 138,500 35,640 19 7 5.2
41-50 23 46.7 135,500 20,240 12 11 2.9
51-60 18 44.3 132,600 7,920 5 14 1.2
>60 2 42.3 129,500 440 0 16 0.5
Total 76 46.2 $74,800 41
Business Data
Month
Orders
Receive
d
$000’’s
Sales
Invoiced
$000’s
Total
kms
Driven
(000’s)
Jul 1,790 1,883 998
Aug 1,665 1,782 928
Sept 1,670 1,680 875
Oct 1,590 1,620 839
Nov 1,515 1,580 836
Dec 1,100 1,540 796
Jan 1,450 1,170 583
Feb 1,680 1,550 795
Mar 1,705 1,650 855

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Apr 1,738 1,680 875
May 1,605 1,783 924
Jun 1,660 1,895 1,008
Total 19,168 19,813 10,312
Customer Data
Customer
Orders
Received
$000’’s
Sales
Invoiced
$000’s
Total kms
Driven
(000’s)
A 11,180 11,650 6,132
B 2,995 3,260 1,707
C 1,395 1,450 755
D 1,055 1,085 570
E 955 986 505
All Others 1,588 1,382 643
Total 19,168 19,813 10,312
a) Gerry, the owner of Gerry’s Transport Pty. Ltd. wants you to respond to the following:
b) Gerry’s company employs 76 drivers. 20 are aged over 50 years, and of these, 5 go to a gym regularly. Of the drivers
under 50 years, 36 attend a gym regularly. As long distance driving is physically demanding Gerry is concerned that
the lack of regular exercise may affect the performance of the over 50 drivers. Gerry has asked you to look at the
available data, specifically gym membership, sick days and Kms. driven, to see if there is any statistical evidence to
show performance is affected by not having gym membership. Respond to Gerry with supporting statistical evidence.
c) Gerry’s pays his drivers a fixed weekly wage, which varies according to age and experience. Some of the drivers are
asking to be paid on a $ rate per kilometre basis as they say the current pay basis favours older drivers and penalises
younger ones. Gerry does not, in principle, have a problem with this, but he would like some statistical data to enable
him to make a decision. Are the younger drivers correct in their assertion? Support your answer with appropriate
statistical data.

ADACC – Chapter 12
d) Gerry has a “gut feeling” that his business is both seasonal and trending downwards. Using the Orders Received and
Sales Invoiced data, identify any seasonality and trend in the 201X year.
e) Gerry would like to see in graphical form
 a comparison of sales invoiced by customer with orders received by customer, and
 Amount invoiced by kilometre by customer
Create illustrative graphs and add any comments that Gerry might be interested in.
f) Undertake your own internet research to answer the following questions:
i. In Gerry’s Driver Data the average wage for a truck driver was quoted as $46,200 p.a. Is this amount realistic
currently? Reference your sources.
ii. Was the sales amount invoiced per Km to Gerry’s customers realistic in today’s economic climate? Again
reference your sources.

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(b)
Sick days
H0: There is no significant difference between gym membership and sick days.
H1 There is significant difference between gym membership and sick days.
SUMMARY
OUTPUT
Regression Statistics
Multiple R 1.29E-08
R Square 1.67E-16
Adjusted R
Square -1
Standard Error 3.265986
Observations 3
ANOVA
df SS MS F
Significan
ce F
Regression 1
1.78E-
15
1.78E-
15
1.67E-
16 1
Residual 1
10.6666
7
10.6666
7
Total 2
10.6666
7
Coefficien
ts
Standar
d Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 8.333333
4.38509
1
1.90037
9
0.30837
6 -47.3845
64.051
2
-
47.384
5
64.051
2
Gym -1.1E-17 0.32991 -3.4E- 1 -4.19196 4.1919 - 4.1919

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Membership 4 17 6
4.1919
6 6
Regression is the one of the most important tool that is used to identify relationship between
dependent and independent variables (Chatterjee and Hadi, 2015). In the above table it can be observed that
value of R is 1.29 which means that sick days and gym membership are not closely related to each other.
Value of level of significance is P= 1>0.05 which means that there is no significant difference between
variables and in this way null hypothesis accepted.

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Turnover
H0: There is no significant difference between gym membership and turnover.
H1 There is significant difference between gym membership and turnover.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.632343
R Square 0.399857
Adjusted R
Square -0.20029
Standard Error 3.55176
Observations 3
ANOVA
df SS MS F
Significan
ce F
Regression 1 8.405 8.405 0.66627 0.564187
Residual 1 12.615 12.615
Total 2 21.02
Coefficien
ts
Standar
d Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 9.314286
4.76878
7
1.95317
7
0.30124
2 -51.2789
69.9074
7
-
51.278
9
69.9074
7
Gym
Membership -0.29286
0.35878
2
-
0.81625
0.56418
7 -4.85161 4.2659
-
4.8516
1 4.2659
Regression results are indicating that value of R square is 0.63 which means that there is moderate
correlation between gym membership and employees turnover. However, value of level of

ADACC – Chapter 12
significance is P = 0.56>0.05 which means that there is no significant difference between variables.
Null hypothesis accepted. Value of beta is -0.29 which means that with increase in gym
membership turnover reduced.
Thus, it can be said that gym membership has impact on employee’s turnover rate but their
sickness frequency does not get affected by the gym membership.
©
Age Number
Ave
Ave.
kms. /
Driver
/ Year
Total $
Fines
for
Group
Ave.
Sick
Days /
Year /
Drive
r
Ave
Turnover
%
Ave.
KM /
Driver
Annua
l Wage
$000’s
Gym
Membership
21-
30 6 43.5 141,000 10,560 5 7 9.3 23500
31-
40 27 46.2 138,500 35,640 19 7 5.2 5129.63
41-
50 23 46.7 135,500 20,240 12 11 2.9 5891.304
51-
60 18 44.3 132,600 7,920 5 14 1.2 7366.667
>60 2 42.3 129,500 440 0 16 0.5 64750
Total 76 46.2 $74,80
0 41 0
Drivers rightly said that they are not getting pay according to their work as it can be seen from the
table given above that average KM per driver is high for those that are in the age group of 21 to 30.
Per driver KM is 23500 and pay is $43.5. On other hand, those who are in the age group of 31 to 40
drive 5129 KM each and pay received by them us $46.2. Thus, they drive very less but receive
higher pay then 21 to 30 age group individuals. In case of 41 to 50 age group per driver drive 5891
KM and pay they receive is $46.7 which is higher then those who are in 21 to 30 age group. In case

ADACC – Chapter 12
of 51 to 60 age group per person drive 7366 KM and pay they receive is $44. In case of those who
are above 60 per drive 64750 KM but receive only $4. Thus, those who are in least and highest age
group drive more and receive less amount. Thus, it can be said that driver saying right that they are
not receiving right amount.
(D)
Jul Aug Sept Oct Nov Dec Jan Feb Mar Apr May Jun
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Order and sales
Orders Received Sales Invoiced $000’s
Figure 2Order and sales fluctuation
It can be seen from the chart that demand is seasonal as in the month of December sharp dip is
observed in the order received and sales invoice. Up to December month consistently sales decline
but after this month again demand elevate.
€

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A B C D E
0
2000
4000
6000
8000
10000
12000
14000
Order received and sales invoiced
Orders Received Sales Invoiced $000’s
Figure 3Comparison of sales and order

ADACC – Chapter 12
A B C D E
0
2000
4000
6000
8000
10000
12000
14000
Order received and sales invoiced
Orders Received Sales Invoiced $000’s
Figure 4Amount by KM by customer
In case of customer A and B there is high amount of order received and sales invoice and in
case of another sales invoice and order received both are low.

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A B C D E All Others
-15%
-10%
-5%
0%
5%
10%
15%
4%
9%
4% 3% 3%
-13%
Sales percentage difference from order received
Figure 5Sales percentage difference from order received
Garry might be interested in knowing margin that is earned on customers. Apart from A, B, C, D
and E customer’s loss is observed in case of all others.
(f)
(1)
Amount paid to the truck drivers is realistic because in Australia average payment made to the
drivers in a year is $52,475 (Truck driver salary in Australia., 2019).
(2)
Yes, sales amount invoiced per Km to Gerry’s customers realistic in today’s economic climate.

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REFERENCES
Books and Journals
Ho, A.D. and Yu, C.C., 2015. Descriptive statistics for modern test score distributions: Skewness,
kurtosis, discreteness, and ceiling effects. Educational and Psychological
Measurement, 75(3), pp.365-388.
George, D. and Mallery, P., 2016. Descriptive statistics. In IBM SPSS Statistics 23 Step by Step (pp.
126-134). Routledge.
Goos, P. and Meintrup, D., 2015. Statistics with JMP: graphs, descriptive statistics and probability.
John Wiley & Sons.
Pyrczak, F., 2016. Making sense of statistics: A conceptual overview. Routledge.
LaFlair, G.T., Egbert, J. and Plonsky, L., 2015. A practical guide to bootstrapping descriptive
statistics, correlations, t tests, and ANOVAs. In Advancing quantitative methods in second
language research (pp. 46-77). Routledge.
Young, J. and Wessnitzer, J., 2016. Descriptive statistics, graphs, and visualisation. In Modern
statistical methods for HCI (pp. 37-56). Springer, Cham.
Zhou, H. and et.al., 2016. A new sampling method in particle filter based on Pearson correlation

ADACC – Chapter 12
coefficient. Neurocomputing. 216. pp.208-215.
Verhagen, S.J. and et.al., 2016. Use of the experience sampling method in the context of clinical
trials. Evidence-based mental health. 19(3). pp.86-89.
Chatterjee, S. and Hadi, A.S., 2015. Regression analysis by example. John Wiley & Sons.
Online
Truck driver salary in Australia., 2019. [Online]. Available through:<
https://au.neuvoo.com/salary/?job=truck+driver>.