Topic: Measures of Central Tendency

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QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency

Compute the sample mean, variance, standard deviation, covariance, and correlation for the given data.

Question

b) Use the sample data below to answer the following questions:

Required:
i) Calculate the sample mean, variance, and standard deviation for . (5 marks)
ii) Calculate the sample mean, variance, and standard deviation for $Y$ . (5 marks)
iii) Calculate the sample covariance between and . (3 marks)
iv) Calculate the sample correlation between and $Y$ . (3 marks)

Answer

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Tags: Correlation, Covariance, Sample Mean, Standard Deviation, Variance
Level: Level 1

Topic: Data Collection, Measures of Central Tendency
Series: MAY 2016

QT – Nov 2017 – L1 – Q4 – Data Collection | Measures of Central Tendency | Measures of Dispersion

Analyze the frequency distribution of access time to a medical consultant, draw an ogive, and calculate measures of central tendency.

Question

Data on access time, in minutes, to a medical consultant who charges by the hour was recorded by his accountant’s assistant over a period of one week. Using a class width of 4 minutes, the following frequency distribution table was obtained:

Access Time (Minutes)	Number of Patients
15 – 19	2
20 – 24	5
25 – 29	8
30 – 34	10
35 – 39	13
40 – 44	17
45 – 49	20
50 – 54	16
55 – 59	12
60 – 64	15

Required:
a) Using a graph sheet, draw a less than or a greater than (more than) cumulative frequency curve (ogive) of the data. (6 marks)
b) From the ogive in (a) above, estimate the median access time. (2 marks)
c) Calculate the mean and the mode of the access times. (6 marks)
d) Calculate the standard deviation of the distribution. (4 marks)
e) Using the values in (b) and (c) above, comment on the skewness of the distribution. (2 marks)
(Total: 20 marks)

Answer

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Tags: Frequency Distribution, Mean, Median, Mode, Ogive, Skewness, Standard Deviation
Level: Level 1

Topic: Data Collection, Measures of Central Tendency, Measures of Dispersion
Series: NOV 2017

QT – May 2017 – L1 – Q5 – Measures of Central Tendency

Create a frequency table and compute measures of central tendency and dispersion from given data.

Question

The mileages recorded for a sample of company vehicles during a given week gave the following data:

Required:

a) Draw the frequency table of this data, given a class size of 5.
(6 marks)

b) Determine the mean, median, and mode for the data and comment on the distribution.
(6 marks)

c) Compute the quartile deviation.
(4 marks)

d) Determine the standard deviation for the data.
(4 marks)

Answer

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Tags: Frequency Distribution, Mean, Median, Mode, Quartile Deviation, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2017

QT – May 2016 – L1 – Q1 – Measures of Central Tendency

This question calculates measures of central tendency and dispersion for fuel gallon consumption in 2010, followed by an interpretation of the results.

Question

Mr. Boo, a Chartered Accountant, is investigating the distribution of the number of fuel gallons consumed per day in the year 2010. He conducted a survey on the number of fuel gallons consumed per day and recorded the following results:

NUMBER OF FUEL GALLONS	PERCENTAGE OF CONSUMPTION
0 but under 5	38%
5 but under 10	25%
10 but under 15	16%
15 but under 20	21%

Required:

a) Calculate the following measures of central tendency: i) Mean (3 marks) ii) Median (3 marks) iii) Mode (3 marks)

b) Compute the following measures of dispersion and skewness: i) Inter-Quartile Range (3 marks) ii) Variance (3 marks) iii) Appropriate coefficient of skewness (3 marks)

c) Using (a) and (b) above, comment on the distribution of the number of fuel gallons consumed per day in 2010 (2 marks).

(Total: 20 marks)

Answer

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Tags: Central Tendency, Dispersion, Inter-Quartile Range, Mean, Median, Mode, Skewness, Variance
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2016

QT – Nov 2016 – L1 – Q5 – Measures of Central Tendency

Analyze the returns on two investments using central tendency, dispersion, and provide a decision based on the results.

Question

Suppose that Mr. Kuu, a retired chartered accountant, is facing a decision about where to invest the remaining small fortune after deducting the anticipated expenses for the next year from his consultancy earnings. An investment analyst has suggested two types of investments, and to help make the decision, he obtained some rates of return from each type. He would like to know what he can expect by way of the return on his investment, as well as other types of information, such as whether the rates are spread out over a wide range (making the investment risky) or are grouped tightly together (indicating a relatively low risk). The returns for the two types of investments are listed below:

If he decides to group the returns according to classes 19-10, 9-0, 1-10, 11-20, 21-30, 31-40 :

Required:

a) Draw histograms for each set of returns. (5 marks)
b) Compute the following measures of central tendency for the set of returns:
i) Mean (3 marks)
ii) Median (3 marks)
iii) Mode (3 marks)
c) Compute the following measures of spread for the set of returns:
i) Standard deviation (3 marks)
ii) Coefficient of variation (2 marks)
d) Based on (a), (b), and (c), which investment should Mr. Kuu choose and why? (1 mark)

Answer

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Tags: Central Tendency, Dispersion, Histograms, Investment Analysis, Risk Assessment
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2016

QT – May 2018 – L1 – Q6b – Measures of Central Tendency

Calculation of central tendency measures and coefficient of variation based on bi-weekly income data.

Question

The table below shows the range of bi-weekly income of a sample of 50 accountants of a multi-national accounting firm:

Range of Income (GH₵)	Number of Accountants
80 and Less than 100	5
100 and less than 120	4
120 and less than 150	12
150 and less than 170	7
170 and less than 200	8
200 and less than 250	9
250 and less than 300	5

Required:
i) Compute all the THREE measures of central tendency of the range of income and comment on the distribution. (8 marks)
ii) Compute the coefficient of variation of the range of income of the accountants. (7 marks)
iii) Interpret your answer in (ii). (1 mark)

Answer

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Tags: Central Tendency, Coefficient of Variation, Dispersion, Mean, Median, Mode, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2018

QT – May 2018 – L1 – Q6a – Measures of Central Tendency

Explanation of measures of central tendency and dispersion with examples.

Question

i) Distinguish between measures of central tendency and measures of dispersion (or variation). (2 marks)

ii) State TWO examples of measures of central tendency. (1 mark)

iii) State TWO examples of measures of dispersion (or variation). (1 mark)

Answer

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Tags: Central Tendency, Dispersion, Mean, Median, Mode, Standard Deviation, Variance
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2018

QT – Nov 2018 – L1 – Q4b – Measures of Central Tendency

Analyze car ownership data by calculating expected value, standard deviation, and creating a relative percentage histogram.

Question

BomBo, a market researcher at a major African Automobile Company (African Moon), classified households by car ownership. The relative frequencies of households for each category of ownership are shown below:

Number of Cars Per Household	Relative Frequencies
0	0.10
1	0.30
2	0.40
3	0.12
4	0.06
5	0.02

Required:
(i) Calculate the expected value of the random variable. (4 marks)

(ii) Calculate the standard deviation of the random variable. (4 marks)

(iii) Draw a Relative Percentage Histogram for the data. (4 marks)

(iv) Using (i)-(iii), comment on the distribution of the data. (3 marks)

Answer

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Tags: Expected Value, Frequency Distribution, Histogram, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2018

QT – Nov 2018 – L1 – Q4a – Measures of Central Tendency

Explain when the mode is preferred as a measure of central tendency over the mean or median.

Question

When is the mode preferred to the mean or the median as a measure of central tendency?

Answer

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Tags: Central Tendency, Mean, Median, Mode
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2018

QT – Nov 2015 – L1 – Q6b – Measures of Central Tendency

Compute the mean, median, mode, and variance from data on textbook expenses.

Question

You have been given the responses of 18 ICAG students to a question on how much they have spent on textbooks in the last month:

Required:
(i) Compute the mean, median, and mode. Comment on the distribution of the responses.
(ii) Compute the inter-quartile deviation, mean deviation, and the standard deviation. Comment on your results.

Answer

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Tags: Inter-quartile Deviation, Mean, Mean Deviation, Median, Mode, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2015

QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency

Compute the sample mean, variance, standard deviation, covariance, and correlation for the given data.

Question

b) Use the sample data below to answer the following questions:

Answer

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Tags: Correlation, Covariance, Sample Mean, Standard Deviation, Variance
Level: Level 1

Topic: Data Collection, Measures of Central Tendency
Series: MAY 2016

QT – Nov 2017 – L1 – Q4 – Data Collection | Measures of Central Tendency | Measures of Dispersion

Analyze the frequency distribution of access time to a medical consultant, draw an ogive, and calculate measures of central tendency.

Question

Access Time (Minutes)	Number of Patients
15 – 19	2
20 – 24	5
25 – 29	8
30 – 34	10
35 – 39	13
40 – 44	17
45 – 49	20
50 – 54	16
55 – 59	12
60 – 64	15

Answer

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Tags: Frequency Distribution, Mean, Median, Mode, Ogive, Skewness, Standard Deviation
Level: Level 1

Topic: Data Collection, Measures of Central Tendency, Measures of Dispersion
Series: NOV 2017

QT – May 2017 – L1 – Q5 – Measures of Central Tendency

Create a frequency table and compute measures of central tendency and dispersion from given data.

Question

The mileages recorded for a sample of company vehicles during a given week gave the following data:

Required:

a) Draw the frequency table of this data, given a class size of 5.
(6 marks)

b) Determine the mean, median, and mode for the data and comment on the distribution.
(6 marks)

c) Compute the quartile deviation.
(4 marks)

d) Determine the standard deviation for the data.
(4 marks)

Answer

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Tags: Frequency Distribution, Mean, Median, Mode, Quartile Deviation, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2017

QT – May 2016 – L1 – Q1 – Measures of Central Tendency

This question calculates measures of central tendency and dispersion for fuel gallon consumption in 2010, followed by an interpretation of the results.

Question

NUMBER OF FUEL GALLONS	PERCENTAGE OF CONSUMPTION
0 but under 5	38%
5 but under 10	25%
10 but under 15	16%
15 but under 20	21%

Required:

a) Calculate the following measures of central tendency: i) Mean (3 marks) ii) Median (3 marks) iii) Mode (3 marks)

b) Compute the following measures of dispersion and skewness: i) Inter-Quartile Range (3 marks) ii) Variance (3 marks) iii) Appropriate coefficient of skewness (3 marks)

c) Using (a) and (b) above, comment on the distribution of the number of fuel gallons consumed per day in 2010 (2 marks).

(Total: 20 marks)

Answer

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Tags: Central Tendency, Dispersion, Inter-Quartile Range, Mean, Median, Mode, Skewness, Variance
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2016

QT – Nov 2016 – L1 – Q5 – Measures of Central Tendency

Analyze the returns on two investments using central tendency, dispersion, and provide a decision based on the results.

Question

If he decides to group the returns according to classes 19-10, 9-0, 1-10, 11-20, 21-30, 31-40 :

Required:

Answer

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Tags: Central Tendency, Dispersion, Histograms, Investment Analysis, Risk Assessment
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2016

QT – May 2018 – L1 – Q6b – Measures of Central Tendency

Calculation of central tendency measures and coefficient of variation based on bi-weekly income data.

Question

The table below shows the range of bi-weekly income of a sample of 50 accountants of a multi-national accounting firm:

Range of Income (GH₵)	Number of Accountants
80 and Less than 100	5
100 and less than 120	4
120 and less than 150	12
150 and less than 170	7
170 and less than 200	8
200 and less than 250	9
250 and less than 300	5

Answer

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Tags: Central Tendency, Coefficient of Variation, Dispersion, Mean, Median, Mode, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2018

QT – May 2018 – L1 – Q6a – Measures of Central Tendency

Explanation of measures of central tendency and dispersion with examples.

Question

i) Distinguish between measures of central tendency and measures of dispersion (or variation). (2 marks)

ii) State TWO examples of measures of central tendency. (1 mark)

iii) State TWO examples of measures of dispersion (or variation). (1 mark)

Answer

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Tags: Central Tendency, Dispersion, Mean, Median, Mode, Standard Deviation, Variance
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2018

QT – Nov 2018 – L1 – Q4b – Measures of Central Tendency

Analyze car ownership data by calculating expected value, standard deviation, and creating a relative percentage histogram.

Question

Number of Cars Per Household	Relative Frequencies
0	0.10
1	0.30
2	0.40
3	0.12
4	0.06
5	0.02

Required:
(i) Calculate the expected value of the random variable. (4 marks)

(ii) Calculate the standard deviation of the random variable. (4 marks)

(iii) Draw a Relative Percentage Histogram for the data. (4 marks)

(iv) Using (i)-(iii), comment on the distribution of the data. (3 marks)

Answer

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Tags: Expected Value, Frequency Distribution, Histogram, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2018

QT – Nov 2018 – L1 – Q4a – Measures of Central Tendency

Explain when the mode is preferred as a measure of central tendency over the mean or median.

Question

When is the mode preferred to the mean or the median as a measure of central tendency?

Answer

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Tags: Central Tendency, Mean, Median, Mode
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2018

QT – Nov 2015 – L1 – Q6b – Measures of Central Tendency

Compute the mean, median, mode, and variance from data on textbook expenses.

Question

You have been given the responses of 18 ICAG students to a question on how much they have spent on textbooks in the last month:

Answer

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Tags: Inter-quartile Deviation, Mean, Mean Deviation, Median, Mode, Standard Deviation
Level: Level 1