Question

The following data is the temperature in August in 50 states in Country ABC.

90	171	202	178	147	102	153	197	127	82
157	185	90	116	172	111	148	213	130	165
141	149	206	175	123	128	144	168	109	167
95	163	150	154	130	143	187	166	139	149
108	119	183	151	114	135	191	137	129	160

1. Construct a frequency distribution and a percentage distribution that have class intervals with the upper class boundaries $99, $119, and so on
2. Construct a cumulative percentage distribution
3. Around what amount does the monthly electricity cost seem to be concentrated?

Answer 1

Solution

Part (a)

Class Interval	Frequency - f	Percentage
80 - 99	4	8
100 - 119	7	14
120 - 139	9	18
140 - 159	12	24
160 - 179	10	20
180 - 199	5	10
200 - 219	3	6
Total	50	100

Answer 1

Part (b)

Class Interval	Cumulative Percentage
80 - 99	8
100 - 119	22
120 - 139	40
140 - 159	64
160 - 179	84
180 - 199	94
200 - 219	100

Answer 2

Part (c)

To answer this question, we will compute the mean = [Σ(i = 1 to 7){xi.fi}]/[Σ(i = 1 to 7){fi}], where

xi and fi are respectively the class mark and frequency of the ith class interval.

Class Interval	Frequency - f	Class Mark - x	x.f
80 - 99	4	89	356
100 - 119	7	109	763
120 - 139	9	129	1161
140 - 159	12	149	1788
160 - 179	10	169	1690
180 - 199	5	189	945
200 - 219	3	209	627
Total	50		7330

So, mean = 7330/50 = 146.

Thus, the temperature seems to be concentrated around 146 Answer 3

NOTE

The question says, ‘monthly electricity cost’, which is possibly a typo.

DONE