Statistics – Page 5 – NBC Institute

QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

Question

A business school preparing candidates for professional examinations conducted a mock examination to ascertain the level of preparedness of its candidates in two subjects: Quantitative Techniques in Business (QTB) and Management Information (MI). The table below gives the scores of twelve selected candidates.

Candidates	1	2	3	4	5	6	7	8	9	10	11	12
Score in QTB (x)	35	77	95	28	76	80	90	62	39	65	90	37
Score in MI (y)	50	82	89	58	65	61	84	59	48	53	80	52

Required:
i. Calculate the Spearman’s rank correlation coefficient between $x$ and $y$ . (9 Marks)
ii. Comment on the result in (i) above. (1 Mark)

Answer

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Tags: Correlation, Mock Examination Scores, Spearman’s Rank
Level: Level 1

Topic: Statistics
Series: NOV 2014

QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

Question

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months)	1	2	3	4	5
Probability of failure	0.10	0.30	0.35	0.20	0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

45% chance of receiving ₦5,000 from her sister,
33% chance of receiving ₦8,000 from her brother,
16% chance of receiving ₦11,000 from her aunt,
6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

Answer

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Tags: Cost Calculation, Expected Value, Financial planning, Probability Distribution
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

Question

Two Chartered Accountants: X and Y, were requested to rank ten banks A, B, C, D, E, F, G, H, I, J according to their performances during a financial year. X ranked the banks as follows:

X’s Rankings: E, B, G, A, C, D, H, F, J, I
Y’s Rankings: E, C, A, B, G, H, J, D, F, I

Calculate the Spearman’s rank correlation coefficient between X and Y and interpret your result.

Answer

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Tags: Rank Correlation, Spearman's Coefficient\
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

Question

a. A fleet of lorries A, B, and C are loaded with blocks meant for a building site.
Lorry A carries of all the needed blocks, B carries of what lorry A carries, and lorry C carries the rest. Lorries A, B, and C contain 13%, 15%, and 11% damaged blocks, respectively.

By drawing a suitable tree diagram, calculate:
i. The proportion of damaged blocks in the fleet. (8 Marks)

ii. The probability of randomly taking a damaged block from lorry B. (2 Marks)

Answer

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Tags: Damaged Blocks, Probability, Tree Diagram
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

Question

i. A six-sided and fair die is thrown into the air. What is the probability:

Of NOT getting a SIX?
That either a THREE, a FOUR, or a FIVE will fall uppermost?
Of obtaining an even number?
(5 Marks)

ii. A block-making factory produces TWO types of blocks: 6-inch and 9-inch. ONE quarter of its output on a particular day are 6-inch blocks, while the remaining three-quarters are 9-inch blocks. If samples of 3 are taken at random, what is the probability of obtaining:

One 6-inch block?
Two 6-inch blocks?
One or two 6-inch blocks?
(5 Marks)

Answer

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Tags: Block Manufacturing, Dice, Probability, Sampling
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

Question

A ten-year record of cocoa production in a certain farm is tabulated as follows:

Year	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012
Production (tonnes)	42	52	41	48	64	67	77	66	73	89

Based on a 4-year moving total, the centered moving average for the year 2007 is:
A. 79.5
B. 69.5
C. 59.5
D. 49.5
E. 39.5

Answer

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Tags: Business Statistics, Moving Average, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q17 – Statistics

This question checks the range of values for the correlation coefficient r.

Question

If $r$ is the correlation coefficient calculated for a bivariate data, then which one of the following is correct?

A. $1$
B.
C.
D.
E.

Answer

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Tags: Bivariate Data, Business Statistics, Correlation
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

Question

Which of the following is NOT TRUE about Normal Distribution?
A. Normal distribution is a frequency distribution.
B. Both tails of the distribution approach but never meet the horizontal axis.
C. It is a probability distribution of a continuous variable that fits many naturally occurring distributions.
D. The exact shape of the normal curve depends on the mean of the distribution.
E. The area under the normal curve represents the probability and totals 1 or 100%.

Answer

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Tags: Business Statistics, Normal distribution, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q15 – Statistics

This question involves calculating the probability that a defective item is from process B.

Question

A large batch of components of TV sets is stocked by a company. The batch comprises components that are manufactured by processes A, B, and C. There are twice as many components from process A as from each of processes B and C in a batch. Components from A contain 8% defectives, and those from B and C contain 11% and 14% defectives respectively.
The probability that a defective item is from process B is:
A. 0.228
B. 0.238
C. 0.248
D. 0.258
E. 0.268

Answer

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Tags: Business Mathematics, Defective Items, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

Question

The TWO components of a Time Series which are usually estimable are:
A. Trend and Cyclic variation
B. Seasonal variation and Trend
C. Random movements and Trend
D. Seasonal variation and Random movements
E. Cyclic variation and Seasonal variation

Answer

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Tags: Forecasting, Seasonal Variation, Time series, Trend
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2015 – L1 – SA – Q17 – Statistics

Identifying the incorrect statement regarding properties of standard deviation.

Question

The following are properties of standard deviation EXCEPT:

A. The greater the spread of the data, the larger the value of the standard deviation
B. The value of standard deviation equals zero seems unlikely except when all observations take the same value
C. Standard deviation takes into account all items in the data set
D. Standard deviation cannot be used for further statistical analysis
E. Standard deviation is not influenced by the size and unit of measurement

Answer

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Tags: Deviations, Mean, Statistical Properties
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q16 – Statistics

Identifying the algebraic sum of deviations from the mean in a dataset.

Question

The algebraic sum of the deviations of a set of numbers from their mean is:

A. The mean of the numbers
B. The modal number
C. The median of the numbers
D. Zero
E. One

Answer

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Tags: Deviations, Mean, Statistics
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q15 – Statistics

Identifying the alternative name for a cumulative frequency curve.

Question

A cumulative frequency curve is also known as:

A. Lorenz curve
B. Cumulative frequency graph
C. Ogive
D. Cumulative frequency line
E. Frequency polygon

Answer

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Tags: Cumulative Frequency, Ogive, Statistical Graphs
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

Question

Which of the following represents the types of variations in time series analysis?

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer

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Tags: Time series, Trend Analysis, Variations
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q12 – Statistics

Identifying the correct term for the amount of time activities can be delayed in project management.

Question

The amount of time during which a path of activities could be delayed without affecting the overall project duration is called:

A. Independent float
B. Total float
C. Free float
D. Excess time float
E. Average time float

Answer

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Tags: Analysis, Statistical Methods, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

Question

The following methods are used to measure the trend of a time series EXCEPT:

A. Semi-average
B. Moving average
C. Free-hand
D. Deseasonalisation
E. Least squares

Answer

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Tags: Statistical Methods, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q10 – Statistics

Calculating Spearman’s rank correlation between price and age of cars.

Question

The following values are computed from a set of bivariate data relating the price and age of 12 selected cars from a car dealer shop as where $d_{i}$ is the difference between ranks of price and age of cars. The computed Spearman’s rank correlation coefficient between the price and age of the car is:

A. -0.4545
B. -0.3535
C. 0.0000
D. 0.3535
E. 0.4545

Answer

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Tags: Bivariate Data, Correlation, Spearman’s Rank Correlation
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q8 – Statistics

Determining the probability of receiving mutilated notes from a specific cashier using a tree diagram.

Question

The following tree diagram shows the scenario with two cashiers (A and B) at a bank where $M$ represents mutilated notes and $N$ represents new notes.

If a customer received mutilated notes, what is the probability that she was paid by cashier A?

A. 0.54
B. 0.55
C. 0.56
D. 0.59
E. 0.61

Answer

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Tags: Conditional Probability, Probability, Tree Diagram
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q7 – Statistics

Calculating how many times two events can occur together.

Question

If an event can occur $m$ times and another event can occur $n$ times, then both events can occur together in:

A. times
B. times
C. $n$ times
D. times
E. times

Answer

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Tags: Combinatorics, Event Occurrence, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2015

Topic: Statistics

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QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

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QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

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QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

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QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

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QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

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QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

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QTB – May 2017 – L1 – SA – Q17 – Statistics

This question checks the range of values for the correlation coefficient r.

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QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

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QTB – May 2017 – L1 – SA – Q15 – Statistics

This question involves calculating the probability that a defective item is from process B.

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QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

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QTB – May 2015 – L1 – SA – Q17 – Statistics

Identifying the incorrect statement regarding properties of standard deviation.

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QTB – May 2015 – L1 – SA – Q16 – Statistics

Identifying the algebraic sum of deviations from the mean in a dataset.

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QTB – May 2015 – L1 – SA – Q15 – Statistics

Identifying the alternative name for a cumulative frequency curve.

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QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

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QTB – May 2015 – L1 – SA – Q12 – Statistics

Identifying the correct term for the amount of time activities can be delayed in project management.

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QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

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QTB – May 2015 – L1 – SA – Q10 – Statistics

Calculating Spearman’s rank correlation between price and age of cars.

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QTB – May 2015 – L1 – SA – Q8 – Statistics

Determining the probability of receiving mutilated notes from a specific cashier using a tree diagram.

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QTB – May 2015 – L1 – SA – Q7 – Statistics

Calculating how many times two events can occur together.

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