Business Statistics

Business Statistics Types of Statistics  

Descriptive: collecting, summarising and describing data. Process includes; collect data, present data, characterize data (e.g. mean) Inferential: drawing conclusions and or making decision concerning a population based on a sample data. Process includes; estimation (estimate the population mean using the sample mean), hypothesis testing.

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Population: collection of all possible individuals, objects or measurements of interest. Sample: a portion of the population of interest.

Four Levels of measurement of data

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Nominal: data that is classified into non-overlapping categories and cannot be arrange in any particular order. E.g. eye color, gender, brand of tv Ordinal level: data that is classified into non-overlapping categories in which ranking is implied. E.g. test performance grand (A,B,C,D,E,F) Interval level: is an ordered scale in which the difference between measurements is a meaningful quantity but the measurements do not have a true zero point. E.g. shoe size (zero has a value) Ratio level: the interval level with an inherent zero starting point. (Zero is significant) e.g. price, distance travelled, time taken.

Graphical presentation of quantitative/ numerical data    

Scatter plot: a plot or graph of pairwise data from two continuous variables, to explore the relationship between them. Pie Chart: a circular display of data where the area of the whole pie represents 100% of the data Bar Chart: a graph in which a bar shows each category. (categorical data) Histogram: a type of vertical bar where the area of each bar is equal to the frequency of the corresponding interval. (quantitative data)

Data collection  

Cross section: data is collected at one point in time. E.g. stock price on the same day Time-series: data is collected over. E.g. stock price on a numerous amount of days.

Measures of Central Tendency Mean   

∑ indicates the operation of adding. ∑x is the sum of the x values in the population Affected by extreme values Not used for ordinal and nominal data

Median  

Is the middle value of a set of numbers after they have been arranged in order. Applicable for ordinal, interval and ratio data, unaffected by extremely larger and extremely small values

Mode  

Is the most frequently occurring value in a data seat It is applicable to all levels of data measurement (nominal, ordinal, interval and ratio)

Measure of Dispersion/Spread 

Describes the spread/variability of a set of data and include; range, variance, standard deviation, coefficient of variation (CV), Z scores, IQR.

Range 

The difference between the largest and the smallest values in a set of data.

Variance 

Is the average of the squared deviations from the arithmetic mean.

Standard Deviation   

Is the square root of the variance For populations whose values are dispersed from the mean, the population variance and standard deviation will be large. (X-Mean)=Standard deviation

1. Calculate the mean 2. Calculate the distance of each observation from the mean and square that difference 3. Sum all the squared differences calculated in step 2 4. Divide the sum of the squared differences. 5. Take the square root of variance calculate in previous step to get standard deviation  Variance and standard deviation indicated the variability in the class performance as measured by test scores Sample variance and standard deviation  If the data is a sample then we use

Coefficient of variation  

The ratio of the standard deviation to the mean expressed as a percentage. Measurement of relative dispersion and used to compared standard deviation/variability of datasets with different means.

Z-Score   

A Z score represents the number of SD a value is above or below the mean of a set of numbers. A negative z-score indicated that the item is below average A positive z-score means that the item is above average