Pages: 10 (2063 words) Published: April 23, 2013
ASSIGNMENT 1- BU1007
Question 1

(i) The following data represent the cost of electricity during July 2006 for a random sample of 50 one-bedroom apartment in a large city

Electricity Charge (\$)|
96| 157| 141| 95| 108|
171| 185| 149| 163| 119|
202| 90| 206| 150| 183|
178| 116| 175| 154| 151|
147| 172| 123| 130| 114|
102| 111| 128| 143| 135|
153| 148| 144| 187| 191|
197| 213| 168| 166| 137|
127| 130| 109| 139| 129|
82| 165| 167| 149| 158|
| | | | |
a. Form a frequency distribution and a percentage frequency distribution that have class intervals with upper class limits \$99, \$119 and so on.

82, 90, 95, 96, 102, 108, 109, 111, 114, 116, 119, 123, 127, 128, 129, 130, 130, 135, 137, 139, 141, 143, 144, 147, 148, 149, 149, 150, 151, 153, 154, 157, 158, 163, 165, 166, 167, 168, 171, 172, 175, 178, 183, 185, 187, 191, 197, 202, 206, 213|

Limits (\$)| Frequency| Percentage%|
200-219| 4| 8 (8/50 x100)|
180-199| 7| 14 (14/50 x100)|
160-179| 9| 18 (18/50 x100)|
140-159| 13| 26 (26/50 x100)|
120-139| 9| 18 (18/50 x100)|
100-119| 5| 10 (10/50 x100)|
80-99| 3| 6 (6/50 x100)|
| | |

b. Construct a histogram and a percentage frequency polygon (Use Excel).

| | | | Mid-point| Frequency|
Lower Limit| Upper Limit| Class| Frequency| 200| 0|
200| 219| 200 up to 219| 4| 209.5| 4|
180| 199| 180 up to 199| 7| 209.5| 7|
160| 179| 160 up to 179| 9| 209.5| 9|
140| 159| 140 up to 159| 13| 209.5| 13|
120| 139| 120 up to 139| 9| 209.5| 9|
100| 119| 100 up to 119| 5| 209.5| 5|
80| 99| 80 up to 99| 3| 209.5| 3|
| | | | 209.5| 0|

c. Form a cumulative percentage frequency distribution and draw a cumulative percentage frequency curve. (4 Marks)

Limits (\$)| Frequency| Percentage%| Cumulative Frequency| Cumulative % frequency| | | | 0| 0/50 x 100 = 100|
200-219| 4| 8%| 4| 4/50 x 100 = 8|
180-199| 7| 14%| 11| 11/50 x 100 =22|
160-179| 9| 18%| 20| 20/50 x 100 = 40|
140-159| 13| 26%| 33| 33/50 x 100 =66|
120-139| 9| 18%| 42| 42/50 x 100 =84|
100-119| 5| 10%| 47| 47/50 x 100 = 94|
80-99| 3| 6%| 50| 50/50 x 100 = 100|

| | | | Mid-point| Frequency|
Lower Limit| Upper Limit| Class| Frequency| 200| 0|
200| 219| 200 up to 219| 4| 209.5| 4|
180| 199| 180 up to 199| 7| 209.5| 7|
160| 179| 160 up to 179| 9| 209.5| 9|
140| 159| 140 up to 159| 13| 209.5| 13|
120| 139| 120 up to 139| 9| 209.5| 9|
100| 119| 100 up to 119| 5| 209.5| 5|
80| 99| 80 up to 99| 3| 209.5| 3|
| | | | 209.5| 0|

d. Around what amount does the monthly electricity cost seem to be concentrated? According to the cumulative frequency table, The monthly electricity costs are concentrated at \$140-\$159. The reason being is that, according to the limit \$140-\$150, more people fall in the middle class. Thus the frequency distribution able displays that the weighted average of people who would spend \$140-\$150 for electricity will be at 26%.

(ii) The following data represent the fat contents, in grams per serving, for a sample of 20 chicken sandwiches from fast-food chains:

Fat contents|
7| 23|
8| 30|
4| 25|
5| 19|
16| 29|
20| 29|
20| 30|
24| 30|
19| 40|
30| 56|
| |
a. Compute the sample mean, median, first quartile, and third quartile of the above data. (10 Marks)

Lowest to highest
4, 5, 7, 8, 16, 19, 19, 20, 20, 23, 24, 25, 29, 29, 30, 30, 30, 30, 40, 56 |
Mean
= 4+5+7+8+16+19+19+20+20+23+24+25+29+29+30+30+30+30+40+56
=464/20
=23.2

Median
= (23+24)/2
= 23.5

First Quartile
=(25/100) x 20
=5
=Thus 16 is the first quartile

Third Quartile
= (75/100) x 20...