Business Math

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Business Math
Homework for session 1
Question 1
1. Quota sampling. A technique which is popular in market research. Such a method uses a team of interviewers, each with an appropriate number of subjects to interview. It is quite wide-spread method, especially among social marketing. For example, some clothes producers make such surveys using street interviewers to find out preferences of their customers. 2. Cluster sampling. A non-random method of sampling, used in cases when there is no sampling frame in evidence. Main idea is to select one or several areas, where you will inquire all necessary information. For example, such a practice is used by companies which are producing different kinds of goods for different areas. 3. Stratification. A method which splits a group of people into different parts of groups, depending on which kind of investigation do you have. It is a basis of quota sampling and widely spread nearly at all surveys. Researchers of stratify interviewed groups by gender, age, nationality and race. 4. Simple random sampling. A sampling method where nearly every person has the same chance to be chosen for the investigation. Used in cases when it is necessary to find out basic attitude to smth among huge group of people. For example, “Do you like Coca-Cola?” to check the loyalty to the brand. Question 2

a) A postal questionnaire is far more cheaper method of collecting data than the personal interview. This method could collect much more samples for a short time. At the same time it has low response rate, but even if you would get answers from just 10% of people, it would cost you less time and money than with personal interview method. The personal interview method is good when researcher has some complicated questions to ask and it is possible to get complex answer only after several connected questions during the interview. b) Simple random sampling is quite good because it is simple. Every person has same chances to be chosen for the focus group. However it cant guarantee that chosen group would represent all necessary public straits. At the same time, quota sampling cant be randomized and it is possible that final data would be less representative. However, if the data was classified and gathered well, the information could have very high quality. For example, inquiry questioning of film-goers after the new production.

Question 3
a) (i)

(ii) Other goods: cars, yachts, tv sets
Other services: health services, tourism, intertainment


Question 4
i. Absolute error – difference between an estimated value and its genuine value. Only a maximum error could be calculated. For example: 21.571 is the True value 20.000 is the Recorded Value. Thus: (True value) - (Recorded Value) = Absolute error (21.571) - (20.000) = 1.571 ii. Relative error – absolute error, expressed as a % of the given estimated value. For example, 1,571/21,571 x 100%= 7,28% iii. Compensating error – happens when “fair” rounding has been accomplished. When numbers, subject to compensating errors, are added, the total relative error should be approximately 0. iv. Biased errors – happens when rounding is carried out in one direction. For examples, when we are rounding down some data to the closest high/low number. | Minimum| Estimate| Maximum|

Time/Wage rate| 145hours$4/hr| 150 hours$4/ hr| 155 hours$4.4/hr| Labour costMaterial cost| $580$2550| $600$2600| $682$2650| Total cost| $3130| $3200| $3332|
Quote| $4000| $4000| $4000|
Profit| $668| $800| $870|

Question 5
a) Largest value – 469, smallest – 347, therefore, range – 122 5 classes – 122/5=24.4
345-369 – number of weeks 16
370-394 – number of weeks 8
395-419 – 4 weeks
420-444 – 1 week
445-469 – 11 weeks
Total – 40
b) Cumulative frequency needs to be plotted against class upper bounds

Question 6
a) A component time is best represented by a line diagram.

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