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APPLIED BUSINESS STATISTICS BY TREVOR WEGNER PDF

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Applied Business Statistics By Trevor Wegner Pdf

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Applied business statistics: methods and Excel-based by Trevor Wegner · Applied business statistics: methods and Excel-based applications. by Trevor. Applied business statistics by Trevor Wegner, , available at Book Depository with free delivery worldwide. applied business statistics: methods and excel based applications (pdf) by trevor wegner (ebook). Empowering management students with statistical.

Both factors affect the validity and reliability of statistical findings. Data Quality Data is the raw material of statistical analysis. If the quality of data is poor, the quality of information derived from statistical analysis of this data will also be poor. Consequently, user confidence in the statistical findings will be low.

A useful acronym to keep in mind is GIGO, which stands for garbage in, garbage out. It is therefore necessary to understand what influences the quality of data needed to produce meaningful and reliable statistical results. Data quality is influenced by four factors: the data type, data source, the method of data collection and appropriate data preparation.

Selection of Statistical Method The choice of the most appropriate statistical method to use depends firstly on the management problem to be addressed and secondly on the type of data available. Certain statistical methods are valid for certain data types only.

The incorrect choice of statistical method for a given data type can again produce invalid statistical findings. A random variable is either qualitative categorical or quantitative numeric in nature. Applied Business Statistics. The data is represented by categories only.

The following are examples of qualitative random variables with categories as data: The gender of a consumer is either male or female. An employees highest qualification is either a matric, a diploma or a degree. A company operates in either the financial, retail, mining or industrial sector. Numbers are often assigned to represent the categories e. Such categorical data can therefore only be counted to determine how many responses belong to each category.

Quantitative random variables generate numeric response data. These are real numbers that can be manipulated using arithmetic operations add, subtract, multiply and divide.

The following are examples of quantitative random variables with real numbers as data: the age of an employee e. Numeric data can be further classified as either discrete or continuous. Discrete data is whole number or integer data.

For example, the number of students in a class e. In the area of production planning, managers use statistical forecasts of future demand to determine machine and labour utilisation over the planning period. It enables a user i to assess data quality and ii to select the most appropriate statistical method to apply to the data.

Both factors affect the validity and reliability of statistical findings. Data Quality Data is the raw material of statistical analysis. If the quality of data is poor, the quality of information derived from statistical analysis of this data will also be poor. Consequently, user confidence in the statistical findings will be low. A useful acronym to keep in mind is GIGO, which stands for garbage in, garbage out.

It is therefore necessary to understand what influences the quality of data needed to produce meaningful and reliable statistical results.

Data quality is influenced by three factors: the data type, the source of data and the methods of data collection. The choice of the most appropriate statistical method to use depends firstly on the management problem to be addressed and secondly on the type of data available. Certain statistical methods are valid for certain data types only.

The incorrect choice of statistical method for a given data type can again produce invalid statistical findings. A random variable is either qualitative or quantitative in nature. The data is represented by categories only. The following are examples of qualitative random variables with categories as data: The gender of a consumer is either male or female.

An employees highest qualification is either a matric, a diploma or a degree. A company operates in either the financial, retail, mining or industrial sector. Numbers are often assigned to represent the categories e. Such categorical data can therefore only be counted to determine how many responses belong to each category.

Quantitative random variables generate numeric response data. These are real numbers that can be manipulated using arithmetic operations add, subtract, multiply and divide. Follow these steps to calculate the median for ungrouped raw numeric data: Arrange the n data values in ascending order.

Median The median Me is the middle number of an ordered set of data. Two alternative central location measures are the median and the mode. Applied Business Statistics These two drawbacks require that other measures of central location be considered. Find the median by first identifying the middle position in the data set as follows: It divides an ordered set of data values into two equal halves i.

Thus the median monthly car sales is 34 cars. Thus the median monthly car sales is Based on the sample size. The data is summarised in the numeric frequency distribution and ogive as shown in Table 3. This means that there were five months when car sales were below To Calculate the Median for Grouped Numeric Data Use these methods when the data is already summarised into a numeric frequency distribution or ogive.

The following are illustrative statements that refer to the mode as the central location measure: Colgate is the brand of toothpaste most preferred by households. An approximate median delivery time for parcels is therefore 35 minutes the interval midpoint. This means that half the deliveries occurred within Applied Business Statistics Find the median delivery time of parcels to clients by this courier company. It can be calculated both for categorical data and numeric data. The most common family size is four.

For large samples of discrete or categorical nominal and ordinal-scaled data: It makes no sense. The supermarket frequented most often in Kimberley is Checkers. This identifies the median interval. The median has one major advantage over the mean — it is not affected by outliers.

It is therefore a more representative measure of central location than the mean when significant outliers occur in a set of data. The majority of machine breakdowns last between 25 and 30 minutes. Mode The mode Mo is defined as the most frequently occurring value in a set data. A drawback of the median. Follow these steps to calculate the mode: For small samples of ungrouped data. Thus a median. The midpoint of 35 minutes can be used as the approximate modal courier delivery time.

If the interval to the left of the modal interval has a higher frequency count than the interval to the right of the modal interval. Numeric Descriptive Statistics For large samples of continuous. Which Central Location Measure is Best? A central location measure must be representative of its data values. Applied Business Statistics To calculate a more representative modal value. Outliers Outliers distort the mean but do not affect the median or the mode.

The mode is not influenced by outliers. If the data type is numeric. In such cases. If the shape is bi-modal. The choice depends mainly on i the data type of the random variable being analysed and ii whether outliers are present or not in the data set. The mode also has one main disadvantage: It is a representative measure of central location only if the histogram of the numeric random variable is unimodal i.

The mode has several advantages: It is a valid measure of central location for all data types i. If the data type is categorical. Data Type If the data type is categorical nominal or ordinal scaled. Weighted Arithmetic Mean The weighted arithmetic mean or weighted average is used when different weights are given to each data value to arrive at an average value.

Geometric Mean The geometric mean is used to find the average of percentage change data. Follow these steps to calculate the geometric mean: Multiply all n observations which are percentage changes. Take the nth root of the product. Find the average annual percentage increase in the electricity tariff. R30 at the end of Week 2 and R33 at the end of Week 3. The average weekly percentage change in the share price can be found using the geometric mean. When each data value is calculated from a different base.

The formula for the geometric mean GM is as follows: The lower quartile. These weighted observations are then summed. The middle quartile. Solution Since the duration of each programme differs i. R and R respectively cannot simply be averaged. It divides an ordered data set into two equal halves.

The weighted arithmetic mean must be applied. The upper quartile. R per hour for a second training programme of six hours and R for a two-hour seminar. In formula terms. Applied Business Statistics 1 The arithmetic mean assumes that each data value is equally weighted i. Follow these steps to calculate the weighted arithmetic mean based on a numeric frequency distribution: Each observation.

This sum is then divided by the sum of the weights. Follow these steps to calculate quartiles lower.

Upper limit R14 The maximum salary paid for the job grade is R14 per month. If the quartile position in not an integer. The only difference lies in the identification of the quartile position.

Lower limit R8 The minimum salary paid for the job grade is R8 per month. For a given job grade. Numeric Descriptive Statistics Figure 3. Quartiles are calculated in a similar way to the median.

In formula terms: Each quartile position is determined as follows regardless of whether n is even or odd: Count to the quartile position rounded down to the nearest integer to find the approximate quartile value.

Sort the data in ascending order. Using Formula 3. Applied Business Statistics Example 3. Solution 1 The sorted daily electricity consumption values in ascending order are shown in Table 3. This is the approximate Q3 value. This is the approximate Q1 value. Thus Q3 is found in the This means that the lower quartile. All other terms are identical to those of the median formula. Numeric Descriptive Statistics Use the following steps to calculate quartiles for grouped data from a numeric frequency distribution: A formula similar to the median formula is used to find both the lower and upper quartiles.

The formula is modified to identify either the lower or the upper quartile position. First find the percentile position. Percentiles Percentiles are similar to quartiles. This idea can be extended to find the data value below which any percentage of data values can fall. The lower quartile is the 25th percentile and the upper quartile is the 75th percentile.

Once the percentile position is found. Percentiles are calculated in the same way as quartiles. Range The range is the difference between the highest and lowest data values. Numeric Descriptive Statistics 3. The measures that are commonly used to describe data dispersion are: Widely dispersed data values about their central location indicate low reliability and less confidence in the central location as a representative measure. Figure 3. Variance The variance is a measure of average squared deviation from the central value.

It is the most widely used and reliable measure of dispersion. Follow these steps to calculate a sample variance: Its other drawback is that it provides no information about the clustering of data values between the minimum and maximum data values.

The range. It must be used with care and always examined along with other measures of dispersion. Find the range of the electricity consumption across households in Rustenburg.

To provide meaning.

Find the variance of the electricity consumption across the sample of households in Rustenburg. Numeric Descriptive Statistics Note: Division by the sample size. Since the variance measure is expressed in squared units. This is the purpose of the standard deviation. The symbol s is used to define the sample standard deviation. Standard Deviation The standard deviation is the square root of the variance.

Calculate the squared deviation of each data value from the sample mean and sum them. The symbol s2 is used to define the variance for sample data. To calculate the population variance.

The following interpretation can be applied to the standard deviation. The standard deviation of household electricity consumption in Rustenburg is 8. Solution From Example 3. Almost all households Then the sample standard deviation. Find the standard deviation of the electricity consumption for the sample of households in Rustenburg. It is therefore a very powerful statistic that is used extensively in further statistical analysis. Coefficient of Variation The coefficient of variation CV is a measure of relative variability.

It is calculated as follows: Therefore it is possible. The smaller the CV. A coefficient of variation is always interpreted as a percentage. Numeric Descriptive Statistics The standard deviation. The lower limit of a CV is zero.

It is important to know the shape of the histogram because it affects the choice of central location and dispersion measures to describe the data.

Three common shapes of a unimodal histogram can generally be observed: Applied Business Statistics Solution It is also called a bell-shaped curve or a normal distribution. If a distribution is symmetrical. Symmetrical Distribution A histogram is symmetrical if it has a single central peak and mirror image slopes on either side of the centre position as shown in Figure 3. The median is therefore preferred as the representative measure of central location in right-skewed distributions.

Median Mean Mode x Figure 3. The mean. Only a few houses are likely to be sold within a few days of being marketed. Negatively Skewed Distribution A histogram is negatively skewed or skewed to the left when there are a few extremely small data values outliers relative to the other data values in the sample.

The median is therefore preferred as the representative measure of central location in left- skewed distributions. Numeric Descriptive Statistics Positively Skewed Distribution A histogram is positively skewed or skewed to the right when there are a few extremely large data values outliers relative to the other data values in the sample. It is calculated using the following formula: The greater the difference between these two measures.

As a rule of thumb. The following formula can be used as a guide: A useful approximation formula for skewness is based on the difference between the mean and the median. The further the skewness coefficient deviates from zero in either a negative or a positive direction. The z-score approach A z-score is a standardised unit of measure of a data value. Numeric Descriptive Statistics 2 Since both skewness coefficients are small positive values. Since these values are close to zero.

The quartiles approach An outlier or extreme value is any data value of a numeric variable that lies either a below a lower limit of Q1 — 1. Refer to section 3. No excessive outliers occur in the sample data.

Two methods can be used to identify outliers in a set of data: This rule of thumb is derived from the property that values x of a normally distributed random variable lie within the limits of 3 standard deviations from its mean.

Each z-score is a measure of how far i. Outliers — How to Identify and Treat Them An outlier is an extreme value relative to the majority of values in a dataset. This is called the lower whisker. Follow these steps to construct a box plot: On a horizontal number line.

Outliers must not be included in a dataset used for inferential statistics are they will distort bias the inferential findings that are intended to describe the broader population picture in a true and unbiased way. This is called the upper whisker. Draw a horizontal line from the minimum value position to the Q1 position.

It also highlights the degree of skewness in the data. Their values — and any related information — must be noted and reported separately for further investigation to identify their cause i. Draw another horizontal line from the Q3 position to the maximum value position.

They should then be identified using one of the above methods and removed from the dataset to avoid distorting the numeric descriptive measures such as the mean and standard deviation. Construct a five-number summary table of daily household electricity consumption and display the results in a box plot. Mark the median inside the box at its numeric value position on the number line.

In a box plot. For practical purposes. Follow these steps to observe skewness in a box plot: If a box plot is symmetrical about the median i. In Example 3. If a bi-modal or multi-modal pattern distribution in a histogram is observed. Therefore it is necessary to segment the total sample into separate homogeneous sub-samples based on an identified external influencing factor e.

This will result in more valid. For categorical type data such as gender. The revised mean can now be used to represent central location as it is no longer distorted by the excluded extreme data values. Numeric Descriptive Statistics Refer to breakdown table analysis in Chapter 2. If the shape of the histogram for a numeric random variable is symmetrical bell-shaped then all three measures of central location mean. For numeric type data.

Measures of dispersion and skewness do not exist for categorical data as they have no meaning. Then one of two courses of action is recommended: Option 1: Select the median to represent the measure of central location.

Applied Business Statistics

Option 2: Remove the outlier s from the data set and re-calculate the mean. It is always recommended that the mean be quoted when reporting statistical findings in such instances. The outliers must however. INC data range. For the geometric mean. Refer to Appendix 2 for a flowchart summary of Descriptive Statistics tools. These measures expressed the location.

It shows the appropriate statistical methods for different data types of variables. For qualitative random variables represented by categorical data. It summarises the statistical methods for a single categorical variable.

Each measure was defined and calculated. A method for identifying outliers was described. Measures of spread and skewness 93 Applied Business Statistics.

Numeric Descriptive Statistics Example 3. Compute the descriptive statistical measures for daily household electricity consumption. The influence of data type and the presence of outliers are identified as the primary criteria determining the choice of a suitable numeric descriptive measure to describe sample data.

Solution The output showing all the descriptive statistics measures for daily household electricity consumption is shown in Table 3. Such options are. The chapter ended with an overview of all the exploratory data techniques that are relevant to either a categorical or a numeric random variable.

Applied Business Statistics are not relevant for categorical data.

This identifies valid statistical techniques for each type of random variable i. These descriptive measures — particularly the mean. Only the box plot cannot be produced through Excel. All numeric descriptive measures are appropriate to describe the profile of quantitative random variables. All descriptive measures can be computed in Excel by using either appropriate function keys or the Descriptive Statistics option in the Data Analysis add-in.

A summary flowchart of descriptive statistical tools is given in Appendix 2. Give a reason. Calculate the mean and standard deviation of percentage returns. If the median mass of five parcels for delivery by a courier service is 6. State which measure of central location would be more appropriate. Give a reason for your answer. Compute the coefficient of variation as a consistency index measure. Interpret each descriptive statistics measure. Interpret the plot. Explain your answer. Interpret the range and standard deviation measures.

Applied Business Statistics The following calculations can be performed either manually. Interpret its meaning.

Applied Business Statistics - Methods and Excel-based applications (Paperback, 4th ed)

They were: Assume no extra bicycles can be ordered. Based on the findings in a. Interpret each central location measure. Interpret these quartile values for the human resources manager. The bad debts percentages are as follows: Interpret these.

Numeric Descriptive Statistics a Find the mean and median negotiated percentage wage increases. The values of meals in rand were: Mean Variance Sample size Group 1 76 34 Group 2 64 88 26 a Compute the coefficient of variation of exam scores for each trainee group. Interpret these quartile values. Is the data skewed? If so.

Applied Business Statistics, Methods and Excel-based Applications.pdf

She surveyed a random sample of 50 families and compiled the following numeric frequency distribution: Should the chamber of business send out an advisory note to all furniture retailers based on these sample findings? Use the weighted average formula. The usage per household was: What is that percentage of income value?

For a particular office complex in the Nelspruit CBD. Use the weighted average formula with the midpoint of each interval as xi. What was the average price per car sold by Value Cars last month? Use the geometric mean to find the average annual escalation rate in office rentals for this office complex over the four-year period.

Interpret each measure. Does the data appear to be skewed? What would be the cause of skewness? INC to answer the following questions: The prices are: Give its value and discuss its usefulness. What percentage of the sampled professional engineers does this represent?

Numeric Descriptive Statistics d Find the coefficient of variation for monthly fuel bills. Based on the histogram and frequency distribution in c. INC to find the lower and upper quartiles of monthly fuel bills of motorists. Estimate the most likely total amount of fuel used in litres by all car commuters in Paarl in a month.

Use the bin range given in the database. Interpret each quartile. INC function key. Interpret the profile of the unit selling price of rosebuds for the flower grower.

Compute the ogive to find the cumulative percentages. INC to compute the upper and lower quartiles of the unit selling price of rosebuds. The unit price per rosebud in cents varies according to supply and demand.

Applied business statistics : Methods and Excel-based applications

Applied Business Statistics d Which central location measure would you use to report on the dividend yields of companies? INC to compute the five-number summary table. For each client. For each. Also compute the lower quartile and upper quartile month-end savings balances.

The table below shows the first 10 records only for the sample data of records. Applied Business Statistics 28 X3. Also compute the lower quartile and upper quartile.

The claims ratio is an indicator of cross-subsidisation of members. Provide any evidence based on the findings above to support your comments. The data only the first 10 of records is shown in the table below. She randomly sampled scheme members and recorded the following variables for each member: The chapter provides a brief overview of the basic concepts of probability to help a manager to understand and use probabilities in decision making. This is done through probability theory.

Probability theory describes ways in which uncertainty can be quantified and measured. These are examples of events representing typical probability-type questions: What is the likelihood that a task will be completed within 45 minutes? How likely is it that a product will fail within its guarantee period?

What is the chance of a telesales consultant making a sale on a call? It is therefore necessary to understand the basic concepts and laws of probability to be able to manage uncertainty. Chapter 4 — Basic Probability Concepts 4. Alternatively stated. A probability is the chance. Subjective probabilities cannot be statistically verified and are not used extensively in statistical analysis. There is a Probability theory provides the foundation for quantifying and measuring uncertainty.

It is used to estimate the reliability in making inferences from samples to populations. This type of probability is used extensively in statistical analysis. Where the probability of an event occurring is based on an educated guess.

Complementary probability: This chapter focuses on calculating and interpreting empirically derived objective proba- bilities. Example 4. If an event A cannot occur i. Applied Business Statistics Deriving Objective Probabilities There are three ways in which objective probabilities can be derived: The following example illustrates how managers can quantify uncertain events and use them as a basis for decision making. The sum of the probabilities of all possible events i.

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A probability value lies only between 0 and 1 inclusive i. Table 4. If an event A is certain to occur i. See Excel file C4.

It is called the sample space. Thus there is complete certainty that a randomly chosen motorist will prefer one of these four petrol brands. These frequency counts are used to derive empirical probabilities, since the data was gathered from a survey and organised into a summary table.

Concept 1: The intersection of two events A and B is the set of all outcomes that belong to both A and B simultaneously. Figure 4. The intersection of two simple events in a Venn diagram is called a joint event.

From Table 4. This is shown graphically in the Venn diagram in Figure 4. There is only a 5. Small Small and Service only service only The union of two events A and B is the set of all outcomes that belong to either event A or B or both. Note that the intersection joint event is subtracted once to avoid double counting.

This is shown in the Venn diagram in Figure 4. Small Small and Service 36 service 24 Events are mutually exclusive if they cannot occur together on a single trial of a random Concept 3:What is your opinion of the latest Idols TV series? Using Excel to perform statistical analysis in this text will allow a student: to examine more realistic business problems with larger datasets; to focus more on the interpretation of the statistical findings; and to transfer this skill of performing statistical analysis more easily to the work environment.

There are four types of measurement scales: nominal, ordinal, interval and ratio. Inferential statistics would be used to generalise the sample findings derived from the respondents to reflect the likely views of the entire company of employees. This indicates the strength of the data in terms of how much arithmetic manipulation on the data is possible. For example, the number of students in a class e. By using our website you agree to our use of cookies. How would you rate your chances of promotion after the next performance appraisal?

A few examples follow for illustrative purposes.