DSC2602
EXAM PACK
Assignment Solutions
Questions. Answers
, DSC2602: 2021
SOLUTIONS TO ASSIGNMENT 04
PLEASE NOTE:
• The solutions to all written assignments will only be published on myUnisa under Additional
Resources.
• The solutions given below are only model answers, using the content from Lessons 1 to 3.
There might also be other ways to arrive at the same correct answer.
• This assignment contributes 25% towards your semester mark.
1
,Question 1
QUESTION:
The following frequency distribution table represents the ages of 100 employees of a certain
company:
Age interval Frequency
20 – 29 30
30 – 39 35
40 – 49 20
50 – 59 10
60 – 69 5
1.1 Identify the modal interval for the data set. (1)
1.2 Determine the median interval for the data set. (2)
1.3 Calculate the mean for the data set. (4)
1.4 Calculate the variance for the data set to two decimal places. (3)
[10]
MODEL ANSWER:
1.1 The modal interval is the interval in the data set with the highest frequency. For the
given data set, the 30 – 39 interval has the highest frequency of 35. Therefore, the modal
interval is the [30 – 39] interval.
1.2 To determine the median interval, we find the interval which contains the middle value
of the ordered data set. The median is the
n+1 100 + 1
= = 50,5-th value.
2 2
To identify the 50,5-th value, the cumulative frequency of the data set is shown in the
table below:
Age interval Frequency Cumulative frequency
20 – 29 30 30
30 – 39 35 65
40 – 49 20 85
50 – 59 10 95
60 – 69 5 100
Using the cumulative frequency, we find that the median value falls in the 30 – 39 interval.
Therefore, the median interval is the interval [30 – 39].
2
, 1.3 As we are dealing with grouped data, the mean is calculated using the formula
Pk
fi xi
x̄ = Pi=1
k
.
i=1 fi
You can do the calculations using the normal mode on your calculator or using the
calculator’s statistical mode. The latter method is recommended as it requires less time
and writing. Consult your calculator’s manual on how to determine the mean of a grouped
data set.
For both methods (using the calculator’s normal or statistical mode), we first need to
determine xi , the middle value (or midpoint) of the i-th interval. The middle value is
calculated by adding the lower and the upper limits of the interval and dividing the result
by two. For example, the middle value of the first interval is
20 + 29
= 24,5.
2
Using the calculator’s normal mode, the calculations are summarised in the table below:
Age interval Frequency xi fi xi
20 – 29 30 24,5 735,0
30 – 39 35 34,5 1 207,5
40 – 49 20 44,5 890,0
50 – 59 10 54,5 545,0
60 – 69 5 64,5 322,5
P5 P5
Total i=1 fi = 100 i=1 fi xi = 3 700,0
P5
fi xi = 3 700,0 and 5i=1 fi = 100. Therefore,
P
From the table i=1
P5
fi xi
x̄ = Pi=1 5
i=1 fi
3 700
=
100
= 37 to two decimal places.
Entering the midpoint values on the calculator’s statistical mode according to the calculator’s
manual, directly yields
x̄ = 37.
1.4 The variance, s2 , must be calculated. Without having to re-enter the data, the statistical
mode of your calculator directly yields the standard deviation,
s = 11,4040 to four decimal places.
Therefore, the variance is
s2 = (11,4040)2
= 130,05 to two decimal places.
3
EXAM PACK
Assignment Solutions
Questions. Answers
, DSC2602: 2021
SOLUTIONS TO ASSIGNMENT 04
PLEASE NOTE:
• The solutions to all written assignments will only be published on myUnisa under Additional
Resources.
• The solutions given below are only model answers, using the content from Lessons 1 to 3.
There might also be other ways to arrive at the same correct answer.
• This assignment contributes 25% towards your semester mark.
1
,Question 1
QUESTION:
The following frequency distribution table represents the ages of 100 employees of a certain
company:
Age interval Frequency
20 – 29 30
30 – 39 35
40 – 49 20
50 – 59 10
60 – 69 5
1.1 Identify the modal interval for the data set. (1)
1.2 Determine the median interval for the data set. (2)
1.3 Calculate the mean for the data set. (4)
1.4 Calculate the variance for the data set to two decimal places. (3)
[10]
MODEL ANSWER:
1.1 The modal interval is the interval in the data set with the highest frequency. For the
given data set, the 30 – 39 interval has the highest frequency of 35. Therefore, the modal
interval is the [30 – 39] interval.
1.2 To determine the median interval, we find the interval which contains the middle value
of the ordered data set. The median is the
n+1 100 + 1
= = 50,5-th value.
2 2
To identify the 50,5-th value, the cumulative frequency of the data set is shown in the
table below:
Age interval Frequency Cumulative frequency
20 – 29 30 30
30 – 39 35 65
40 – 49 20 85
50 – 59 10 95
60 – 69 5 100
Using the cumulative frequency, we find that the median value falls in the 30 – 39 interval.
Therefore, the median interval is the interval [30 – 39].
2
, 1.3 As we are dealing with grouped data, the mean is calculated using the formula
Pk
fi xi
x̄ = Pi=1
k
.
i=1 fi
You can do the calculations using the normal mode on your calculator or using the
calculator’s statistical mode. The latter method is recommended as it requires less time
and writing. Consult your calculator’s manual on how to determine the mean of a grouped
data set.
For both methods (using the calculator’s normal or statistical mode), we first need to
determine xi , the middle value (or midpoint) of the i-th interval. The middle value is
calculated by adding the lower and the upper limits of the interval and dividing the result
by two. For example, the middle value of the first interval is
20 + 29
= 24,5.
2
Using the calculator’s normal mode, the calculations are summarised in the table below:
Age interval Frequency xi fi xi
20 – 29 30 24,5 735,0
30 – 39 35 34,5 1 207,5
40 – 49 20 44,5 890,0
50 – 59 10 54,5 545,0
60 – 69 5 64,5 322,5
P5 P5
Total i=1 fi = 100 i=1 fi xi = 3 700,0
P5
fi xi = 3 700,0 and 5i=1 fi = 100. Therefore,
P
From the table i=1
P5
fi xi
x̄ = Pi=1 5
i=1 fi
3 700
=
100
= 37 to two decimal places.
Entering the midpoint values on the calculator’s statistical mode according to the calculator’s
manual, directly yields
x̄ = 37.
1.4 The variance, s2 , must be calculated. Without having to re-enter the data, the statistical
mode of your calculator directly yields the standard deviation,
s = 11,4040 to four decimal places.
Therefore, the variance is
s2 = (11,4040)2
= 130,05 to two decimal places.
3
