Question Tag: Frequency Distribution

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  • 1 Marks

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

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

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

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  • 1 Marks

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

This question calculates the median salary from a salary distribution.

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

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q12 – Data Collection Analysis

Calculates the relative frequency of babies weighing between 4-5 kg.

Given the frequency distribution of weights of babies at the post-natal ward of a University Teaching Hospital as:

Weight (kg) Number of babies
2 – 3 32
4 – 5 17
6 – 7 11

Which of the following values represents the relative frequency of the class 4-5 kg weight of babies in the ward?
A. 0.17
B. 28%
C. 0.283
D. 17%
E. 0.17%

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  • 1 Marks

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

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

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

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  • 1 Marks

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

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

: 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

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  • 1 Marks

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

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

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

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  • 10 Marks

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.

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.

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  • 1 Marks

QTB – Nov 2015 – L1 – SA – Q2 – Data Collection Analysis

This question asks which diagram does not depict information in a frequency distribution.

Which ONE of the following diagrams does NOT depict the information in a frequency distribution for numerical data?

A. Histograph
B. Histogram
C. Bar Chart
D. Frequency Polygon
E. Pie Chart

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  • 20 Marks

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.

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)

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  • 20 Marks

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

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

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)

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  • 1 Marks

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

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

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

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  • 1 Marks

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

This question calculates the median salary from a salary distribution.

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

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q12 – Data Collection Analysis

Calculates the relative frequency of babies weighing between 4-5 kg.

Given the frequency distribution of weights of babies at the post-natal ward of a University Teaching Hospital as:

Weight (kg) Number of babies
2 – 3 32
4 – 5 17
6 – 7 11

Which of the following values represents the relative frequency of the class 4-5 kg weight of babies in the ward?
A. 0.17
B. 28%
C. 0.283
D. 17%
E. 0.17%

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  • 1 Marks

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

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

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

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  • 1 Marks

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

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

: 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

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  • 1 Marks

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

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

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

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  • 10 Marks

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.

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.

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  • 1 Marks

QTB – Nov 2015 – L1 – SA – Q2 – Data Collection Analysis

This question asks which diagram does not depict information in a frequency distribution.

Which ONE of the following diagrams does NOT depict the information in a frequency distribution for numerical data?

A. Histograph
B. Histogram
C. Bar Chart
D. Frequency Polygon
E. Pie Chart

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  • 20 Marks

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.

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)

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  • 20 Marks

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

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

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)

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