Business Statistics - Iloka Benneth Chiemelie

PART A

Question 1 – The uses of statistics in business and economics (10 Marks)

In order to elaborate on the use of statistics in business and economics, it is viewed necessary to first define what statistics is. Statistics is the application of mathematical elements and formulas for designing experiments and other data collection, summarizing information to aid understanding, drawing conclusions from data, and estimating the present or predicting the future. It is a vast field of study that encompasses all other fields of studies such as science, arts, and psychology.

Use of statistics in business

Data sampling in business research – statistics is used in determining the population of a target group for research and sampling the data to the groups. For instance, we use random sampling, a statistical approach where a sample is distributed randomly beginning with one till the nth number. This can further be explained as: if we need a sample of 10 students from Mantissa College for data gathering, we can begin with 1 and proceed with every 2^nd occurring student in the interval until we reach 10 students. This means 1, 3, 5, 7, 9, 11… nth. This is a very good application of statistics in business.

Budgeting in business management – budgeting is an essential element of any business as it helps in determining the profitability of the business. Statistics is used in preparing a financial budget such as income statement to predict how the business will make money. For instance, KFC restaurants can use statistics to determine their potentials for growth by multiplying an estimated average purchase with the total population and market this estimation was based from. By this means, they forecast their expected revenue.

Employee's work rate in payroll management – many businesses nowadays adopt a form of motivational approach in their system where employees are paid a commission based on their work rate and statistics is very crucial in this area of business. In order to determining the percentage of commission and employee will earn per month, business adopt statistical formulae to calculate their working hours, and multiply these hours per percentage of commission. For example, assuming average of 10hours is needed for a commission of 2% of weekly wages, the company can determine the number of hours worked and multiply it against the mean (10 hours) to see if employees are eligible for the commissions.

In economics

Determining of consumption index – in the field of economics, statistics is used to determine the consumption rate of a specific market. Businesses apply this model in other to ensure business equilibrium where demand equals supply. For instance, Coca-Cola can determine the consumption of their soft drinks in Malaysia by comparing the annual statistical data of their total sales for the last 5 years against the population of Malaysia in each year.

Determining GDP per capita of a nation – the only way we can determine the market value of all officially recognized final goods and services produced within a country in a given period is through statistics. GDP per capita measure the purchasing power of a nation against the purchasing of other nations, and it is an essential area of economics as it helps international companies to determine the prices for their goods in each country and also decided in what country they will internationalize.

Determining economic class of people in a country – another area of where statistics is used is in determining the economic distribution of people in a country. For instance, we can group people in a country according to low income earners, medium income earners or high income earners and statistics is essential in this area of economics as it improves our precision based on leveraging collected data according to distributed samples.

Question 2 – for purpose of statistics, distinguish between cross-sectional data and time series data and illustrate their implications for business environment (10 marks)

A cross sectional data is a set of one dimensional data point that involves gathering data by observing numerous objects (for instance, individuals, companies and countries) at the same time or without reference to difference in time. While on the other hand, a time series data is a sequence of data points which are typically measured at a successive time instants and spaced at uniform time interval.

This can be illustrated by the rate of obesity in a country (e.g. Malaysia). In reference to cross sectional data, if we want to know obesity rate in Malaysia, we can take a sample of 1,000 people from a cross section of the population and we can use this sample to determine the number of obese people as a representative of the whole population at a given point in time. Assuming 20% of the sample where found to be bossed, we can assume it is the percentage of obesity in the country but it doesn't tell us about the past nor help in predicting the future.

On the other hand, the case of a time series data will be based on comparing the present rate with previous data gathered at an equal time interval. Assuming we have the rate of obesity for the last five years and we have the data for this current year, we can determine the growth rate of obesity in Malaysia and predict the future growth rate.

Their implications in business

Cross sectional data – it deals only with the present and cannot be used as a guide to the past or predicting the future of any business dealings. Thus, they are unreliable in probability statistics.

Time series data – it combines both the present and the past to determine the current situation in business dealing. Therefore, they can be seen as a reliable form of predicting the future of any business dealing and finding the solutions to any business problem by comparing past events.

Section B

Question 3 - A partial relative frequency distribution is give:

Class	Relative Frequency
A	0.22
B	0.18
C	0.40
D	?

1. What is the relative frequency of class D? (5 Marks)

Relative Frequency in this situation = sum of all relative frequencies / total class

                                                          = 0.80/4 = 0.20

1. The total sample size is 200, what is the frequency of class D? (5 marks)

Frequency of class D = relative frequency of D × 200

                                   = 0.20 × 200 = 40 (i.e., D occurred 40 times).

1. Show the frequency distribution and percent frequency distribution. (15 marks)

Class	Frequency distribution	Percent Frequency Distribution
A	44	22
B	36	18
C	80	40
D	40	20

Question 4 – Consider a sample with the data values of 53, 55, 70, 58, 64, 57, 55, 69, 57, 68 and 53. Compute the mean, median and mode. (10 marks)

First arrange the data = 53, 53, 55, 55, 57, 57, 58, 64, 68, 69, 70   

Mean = 53+53+55+55+57+57+58+64+68+69+70 = 659 = 55.90

                                           11                                       11 

Median = Middle Number = 57

Mode = Elements with highest occurrences = 53, 55 and 57

Question 5 – consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20^th, 25^th, 65^th, and 75^thpercentiles. (10 marks)

Percentile =

First we need to arrange the data = 15, 20, 25, 25, 27, 28, 30, 34

20^th percentile = 20/100 × 8 + ½ = 2.1 (2). Thus, the 20^th percentile by rounding up = 20

25^th percentile = 25/100 × 8 + ½ = 2.5 (3) Thus, the 25^th percentile by rounding up = 25

65^th percentile = 65/100 × 8 + ½ = 5.7 (6) Thus, the 65^th percentile by rounding up = 28

75^th percentile = 75/100 × 8 + ½ = 6.5 (7) Thus, the 75^th percentile by rounding up = 30

Question 6 – Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median. (10 marks)

First arrange the data = 10, 12, 16, 17, 20, 21

Mean = 96/6 = 16

Median = middle number = (16+17)/2 = 16.5

Question 7 – Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28 and 25. Compute the range, variance, and standard deviation. (25 marks)

First arrange the data = 15, 20, 25, 25, 27, 28, 30, 34

Range = largest number – smallest number = 34 – 15 = 19

Variance = first find the mean = 25.5

Variance = (15-25.5) + (20-25.5) + (25-25.5) + (25-25.5) + (27-25.5) + (28-25.5) + (30-25.5) + (34-25.5)

                                                                          8

Variance = (-10.5)² + (-5.5) ² + (-0.5) ² + (-0.5) ² + (1.5) ² + (2.5) ² + (4.5) ² + (8.5) ²

                           8

Variance =                                                       242

                                                                          8

So, the Variance is = 30.25

Standard Deviation: σ = √variance = 5.5