Business Mathematics & Statistics Assignment Q & A

Q.1 (a)         The following table presents the number of new business opened in Pakistan during the third quarter of 1990.  Construct a pie chart to represent these data.

Ans.            To construct the pie chart, we will have to calculate the percentage for each type of new business opened to the total number of businesses opened during the third quarter of 1990 and then angle of each representation will determine in the following manner:

                   The total number of new businesses opened = 31728

                  
Nature of Business

No. of Business





Angle
Retailing
10,724
33.8/100 x 360 =
122°
Services
4,886
15.4/100 x 360 =
55°
Construction
4,315
13.6/100 x 360 =
49°
Wholesaling
3,776
11.9/100 x 360 =
43°
Manufacturing
2,760
8.7/100 x 360 =
31°
Other
5,267
16.6/100 x 360 =
60°
Total:
31,728

360°

                   Now the pie chart will be constructed by dividing a circular pie into six parts of proportional sizes as indicated by the percentages representing them. The pie chart would appear as:


(b)               Why does business statistics usually involve the use of sample data instead of the entire population when making a business decision.

Ans.            Business statistics usually involves the use of sample data instead of the entire population, due to the following reasons.

        In most cases, it is impossible to obtain the data for the entire population. For example, if a TV network wants to obtain the views of its viewers about a certain talk show, it would be practically impossible for the network to reach all of its viewers.

        Sampling saves time, cost, and effort. To gather data about every member of the population is usually very time consuming and costly. Usually, it is so costly that the benefits expected to be achieved from analyzing the data are not worth the cost involved. Therefore, a random sample, which is representative of the population, is chosen.

        In some cases, inspection or testing of a good or product destroys its usefulness. For example, if a firm manufactures bullets, it will not be feasible to test each and every bullet by firing it because then they would become useless. Therefore, in such cases, sampling is unavoidable.



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