Topic: Data Collection Analysis

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QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis

Draw a frequency polygon and an ogive based on gasoline mileage data from an experiment.

Question

In a particular organisation, an experiment which was conducted to determine the gasoline mileage of a particular type of car yielded the following data:

Miles per gallon	Percent
10 and under 12	4
13 and under 15	8
16 and under 18	14
19 and under 21	26
22 and under 24	12
25 and under 27	11
28 and under 30	10
31 and under 33	7
34 and under 36	6
37 and under 39	2

Required:

i. Draw the frequency polygon for gasoline mileage. (5 Marks)
ii. Draw the ogive for gasoline mileage. (5 Marks)

Answer

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Tags: Frequency Polygon, Gasoline Mileage, Graphical Representation, Ogive
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – May 2017 – L1 – SB – Q3b – Data Collection Analysis

Find the regression equation between QTB and FA marks and estimate values.

Question

The table below gives the scores of seven candidates in Quantitative Techniques in Business (QTB) and Financial Accounting (FA) of ICAN Professional Examination:

QTB Marks (y)	50	72	36	64	52	56	80
FA Marks (x)	38	51	19	53	39	38	66

You are required to:
i. Obtain the regression equation if the mark in QTB is regressed on FA. (6 Marks)

ii. Obtain the estimate of mark in QTB, if the mark in FA is 60. (2 Marks)

iii. Obtain the estimate of mark in FA, if the mark in QTB is 75. (2 Marks)

Answer

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Tags: Correlation, Estimation, Regression Equation
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q2b – Data Collection and Analysis

Determine angles for pie chart representation and complete a project network diagram with project duration.

Question

i. The monthly expenditure (₦’000) of a household on some items are given as follows:

Item	Expenditure (₦’000)
Food	50
Transport	25
Utilities	35
Miscellaneous	10

Determine the angle which will represent each item on a pie chart. (6 Marks)

ii. The activities needed to complete a project with their durations (in weeks) are given below:

Activity	Preceding Activity	Duration (weeks)
A	–	4
B	–	6
C	A	8
D	B	12
E	B	11
F	C, D	9

You are required to draw the activity-on-arrow network diagram for the project and determine the duration of the project. (4 Marks)

Answer

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Tags: Critical Path Method, Network Diagram, Pie Chart
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q1b – Data Collection Analysis

Construct a histogram and determine the modal wage from the wage distribution data.

Question

b. The table below shows the weekly wage distribution of artisans in a certain factory:

Weekly Wage (₦’00)	Number of Artisans
38 – 47	16
48 – 57	24
58 – 67	41
68 – 77	53
78 – 87	76
88 – 97	118
98 – 107	224
108 – 117	83
118 – 127	15
128 – 137	4

i. Draw a histogram to represent the wage distribution using the scales: On x-axis, let 1 cm represent ₦100; on y-axis, let 1 cm represent 10 artisans. (4 Marks)

ii. Deduce the modal weekly wage from the histogram. (2½ Marks)

iii. Use the appropriate formula to calculate the modal weekly wage. (3½ Marks)

Answer

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Tags: Histogram, Modal Wage, Wage Distribution
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q12 – Data Collection and Analysis

This question involves calculating the quartile deviation given the first quartile and age distribution.

Question

The age distribution of the administrative staff in a tyre manufacturing company is distributed as follows:

Age of administrative staff (years)	Number of administrative staff
28 and under 34	2
34 and under 40	15
40 and under 46	19
46 and under 52	10
52 and under 58	3
58 and under 64	1

If the first quartile age is 38.2 years, then the quartile deviation of the age distribution is:
A. 3.45 years
B. 4.35 years
C. 4.53 years
D. 5.34 years
E. 5.43 years

Answer

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Tags: Age Distribution, Dispersion, Quartile Deviation
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q11 – Data Collection and Analysis

This question calculates the first quartile age from an age distribution table of artisans.

Question

If the age distribution of the artisans in a tobacco company is tabulated as follows:

Artisan’s age (years)	Number of Artisans
20 and under 25	3
25 and under 30	14
30 and under 35	18
35 and under 40	11
40 and under 45	3
45 and under 50	1

Then the first quartile age is:
A. 28.38 years
B. 28.39 years
C. 28.93 years
D. 29.38 years
E. 29.93 years

Answer

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Tags: Age Distribution, Frequency Distribution, Quartile Calculation
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q10 – Data Collection Analysis

This question involves finding the standard deviation given the variance and mean.

Question

The variance of is 4, and the mean is 5. Find the standard deviation.

A. 2
B. 3
C. 2
D. 3
E. 16

Answer

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Tags: Business Statistics, Dispersion, Mean, Standard Deviation, Variance
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q9 – Data Collection Analysis

This question identifies the reasons why the mean is preferred for statistical calculations.

Question

The mean is the most commonly used statistics for further statistical calculations because it:
A. Tends to lie at the centre of a set of data
B. Is easy to calculate
C. Takes all observations in the data into consideration
D. Is the most popular
E. Is not affected by extreme values in the data

Answer

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Tags: Central Tendency, Mean Calculation, Statistical Calculations
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q8 – Data Collection and Analysis

This question calculates the median salary from a salary distribution.

Question

If the monthly salary of the staff of ABC Plc. is distributed as follows:

Monthly salary (N’000)	Number of staff
6 and under 12	2
12 and under 18	13
18 and under 24	16
24 and under 30	10
30 and under 36	2
36 and under 42	1
Total	44

Then, the median salary is:
A. N20,256
B. N20,265
C. N20,526
D. N20,625
E. N20,652

Answer

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Tags: Business Statistics, Frequency Distribution, Median, Salary Distribution
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – Nov 2014 – L1 – SA – Q14 – Data Collection Analysis

Calculates the mean deviation of a given set of values.

Question

The mean deviation of the values: 7, 8, 10, 14, 25, 30 is:
A. 16.86
B. 14.89
C. 7.89
D. 6.89
E. 5.89

Answer

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Tags: Data Analysis, Mean Deviation, Measures of Central Tendency
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q13 – Data Collection Analysis

Determines the classification of the mode in a given data set.

Question

The mode in the set of data 2, 3, 5, 5, 5, 7, 7, 7, and 6 is described as:
A. Unimodal
B. Bimodal
C. Modal average
D. Trimodal
E. Multimodal

Answer

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Tags: Bimodal, Data Analysis, Mode, Unimodal
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q11 – Data Collection Analysis

Calculates the variance of a grouped data set representing traveling times.

Question

The following data are for the travelling time to and from work in hours per day for a group of factory workers:

No. of hours	No. of workers
Under 1	20
1 up to 2	10
2 up to 3	5
3 up to 4	4

The variance of the data is
A. 1.00
B. 1.01
C. 1.02
D. 1.12
E. 1.22

Answer

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Tags: Frequency Distribution, Travel Time, Variance
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q10 – Data Collection Analysis

Determines the cumulative frequency corresponding to a specific mark in a data set.

Question

: The following are the marks obtained by 10 students in a class mid-term examination: 30%, 40%, 50%, 30%, 30%, 30%, 40%, 60%, 40%, and 30%. The cumulative frequency that corresponds to 50% is:
A. 1
B. 5
C. 8
D. 9
E. 10

Answer

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Tags: Class Marks, Cumulative Frequency, Frequency Distribution
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q9 – Data Collection Analysis

Calculates the first quartile (Q1) of the given frequency distribution.

Question

The table below shows the frequency distribution of marks obtained by 36 students in a class:

Class Marks	Frequencies
0 but less than 5	6
5 but less than 10	10
10 but less than 15	8
15 but less than 20	12

The first quartile of the distribution is:
A. 6.0
B. 6.2
C. 6.3
D. 6.4
E. 6.5

Answer

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Tags: Class Intervals, Frequency Distribution, Quartiles
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis

This question involves calculating moving averages and centered moving averages for quarterly sales data.

Question

The quarterly sales figures of company ABC Plc. for 3 years are as recorded below:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
Year 1	30	34	37	41
Year 2	45	49	54	57
Year 3	59	66	70	74

Required:
i. Calculate:

The moving averages.
(9 marks)

ii. The centered moving average for Quarter 3, Year 1.
(1 mark)

Answer

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Tags: Moving Averages, Seasonal Adjustment, Time series
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q5a – Data Collection Analysis

Calculate the mean, median, and mode for the given distribution of student scores.

Question

A group of 24 final year students participated in an Economic Theory Test and their scores were recorded as follows:

12, 14, 18, 7, 11, 15,
8, 15, 10, 14, 19, 9,
14, 6, 13, 14, 12, 16,
10, 9, 12, 15, 8, 17

Required:

Determine the:

Mean,
Median, and
Mode of this distribution.

(Total: 10 Marks)

Answer

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Tags: Data Analysis, Mean, Median, Mode, Student Scores
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2015

QTB – Nov 2015 – L1 – SB – Q3 – Data Collection Analysis

Calculate the semi-interquartile range and standard deviation for the income distribution of families.

Question

The table below shows the hypothetical incomes of some families in a locality:

Income (N)	Percent (%)
1000 – 1999	6.2
2000 – 2999	5.9
3000 – 3999	7.2
4000 – 4999	8.8
5000 – 5999	7.8
6000 – 6999	15.0
7000 – 7999	17.6
8000 – 8999	12.8
9000 – 9999	8.5
10,000 – 10,999	10.2

Required:

a. Determine the semi-interquartile range for the incomes of the families. (10 Marks)

b. Determine the standard deviation for the incomes of the families. (10 Marks)

(Total: 20 Marks)

Answer

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Tags: Data Analysis, Income Distribution, Semi-Interquartile Range, Standard Deviation
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2015

QTB – May 2015 – L1 – SB – Q5b – Data Collection Analysis

This question requires calculating the lower and upper quartiles for the age distribution of licensed automobile drivers using cumulative frequency.

Question

The following data gives the distribution by age of licensed automobile drivers in a city in the year 2011:

Age Group	Number of Drivers (in thousands)
14 – 19	5
20 – 25	48
26 – 31	124
32 – 37	205
38 – 43	86
44 – 49	72
50 – 55	53
56 – 61	13

You are required to calculate the lower quartile (Q1) and upper quartile (Q3) of the age of the drivers.

Answer

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Tags: Drivers' Age, Frequency Distribution, Quartiles, Statistics
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2015

QTB – Nov 2015 – L1 – SA – Q6 – Data Collection Analysis

This question asks for the simplest measure of dispersion among the listed options.

Question

The simplest measure of dispersion is the:

A. Mean deviation
B. Standard deviation
C. Range
D. Coefficient of variation
E. Mean Absolute Deviation (MAD)

Answer

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Tags: Dispersion, Range, Standard Deviation
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q5 – Data Collection Analysis

This question calculates the mean earnings per hour for employees in a company.

Question

In a company having 100 employees, 80 each earn N800.00 per hour and the remaining 20 each earn N1000.00 per hour. What is the mean earnings per hour?

A. N940 per hour
B. N840 per hour
C. N740 per hour
D. N640 per hour
E. N540 per hour

Answer

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Tags: Earnings, Mean, Measures of Central Tendency
Level: Level 1