Question

Question 1 The following data represent the cost of electricity (in Rand) during July 2019 for a random sample of 30 one-bedroom apartments in a large city:

96 171 202 178 147 197 130 149 167 191 135 129 158 166 150 95 187 144 139 175 123 111 116 202 157 128 82 102 112 95

(a) Construct a stem and leaf graph for the given data. (10)

(b) Construct a histogram for the given data. (10)

(c) Draw a table with the relative frequencies and cumulative frequencies (in percentages) for all class intervals. (10)

(d) Draw a cumulative frequency polygon for the data. (10) In (b), (c) and (d), use the following class intervals: 82 101 142 161 202 221 102 121 162 181 122 141 182 20

Answer 1

(a) STEM and LEAF Graph

STEM	LEAF
8	2
9	5 5 6
10	2
11	1 2 6
12	3 8 9
13	0 5 9
14	4 7 9
15	0 7 8
16	6 7
17	1 5 8
18	7
19	1 7
20	2 2

Here Stem represents the first(or first two digit in case of 3 digit number) and the Leaf represents next digit.

For instance if the number is 82, we write 8 under stem and 2 under leaf,

Similarly if a number is 112 , we write 11 under stem and 2 under leaf.

This is repeated for all the numbers and left between the numbers under LEAF to differentiate between them.

(b) First we group the data into Class Intervals as below -

C.I	Frequency
82-101	4
102-121	4
122-141	6
142-161	6
162-181	5
182-201	3
202-221	2

We use MS Excel for the construction of Histogram. We select the above data and then select Insert in the Menu bar, then we select Histogram . The histogram is plotted as -

(c) To calculate the relative frequency , we use the formula

Relative Frequency = ((Frequency of that particular class) / (Total frequency)) * 100 %

For instance, we want to calculate the relative frequency of 82-101 C.I, the frequency of this class is 4 and the total frequency is 30, so the relative frequency = (4/30) * 100 = 13.33 %.

Similarly for the other C.I as well , we calculate the relative frequency using the same method.

Now to calculate the cumulative frequency , we add up the relative frequency of that particular class and the previous classes.

For instance Cumulative frequency of class 122-141 = 20+13.33+13.33 = 46.66 %

Similarly we calculate the cumulative frequency of the other classes as well.

It is tabulated below -

C.I	Frequency	Relative Frequency	Cumulative Frequency
82-101	4	13.33333333	13.33333333
102-121	4	13.33333333	26.66666667
122-141	6	20	46.66666667
142-161	6	20	66.66666667
162-181	5	16.66666667	83.33333333
182-201	3	10	93.33333333
202-221	2	6.666666667	100

(d) To construct a cumulative frequency polygon on excel , we select the cumulative frequency data and then select Insert in Menu bar and select line graph. It looks like this: