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TREVOR WEGNER. Applied Business. Statistics. METHODS AND EXCEL- BASED Fourth edition (Web PDF) ISBN 1 9 (Web PDF). Applied Business Statistics, Methods and Excel-based lesforgesdessalles.info - Ebook Download as PDF, TXT or read online from Scribd. Flag for . Trevor Wegner. 10 records Methods and Excel-based Applications-Juta ().pdf - Ebook TREVOR WEGNER. Applied Business lesforgesdessalles.info 3 12/18/ AM.
Observation Primary data can be collected by observing a respondent or a process in action. Applied Business Statistics Example 3. Management Questions 1 2 3 4 5 How many shoppers are male and prefer to shop at Checkers? The usage per household was: Only a few houses are likely to be sold within a few days of being marketed. Calculate the mean and standard deviation of percentage returns.
A larger sample of respondents can be reached in a relatively short time. Call-backs can be made if the respondent is not available right away. Surveys are conducted either through personal interviews. Chapter 1 — Statistics in Management studies. The cost is relatively low. People are more willing to talk on the telephone. Surveys are the most common form of data collection in consumer marketing and socio-economic research. The disadvantage of this approach is the passive form of data collection.
Electronic data collection is more reliable and more accurate giving better quality data than manual data-recording methods. Surveys Survey methods gather primary data through the direct questioning of respondents using questionnaires to structure and record the data collection.
This approach offers a number of advantages: E-surveys are significantly cheaper and faster than personal or postal interviews. The anonymity of each respondent is assured. Applied Business Statistics Disadvantages include: An e-survey approach uses the technology of e-mails.
E-surveys are becoming increasingly popular for the reasons listed below: An e-survey automates the process of collating data. They also offer the following advantages over personal interviews: Interviewer bias is eliminated as there is no direct questioning by an interviewer.
The data is current and more likely to be accurate leading to high data quality. They are most suitable when the target population from which primary data is required is geographically dispersed and it is not practical to conduct personal interviews. E-surveys also have similar drawbacks to the traditional postal survey approach. E-surveys have largely replaced postal surveys. Not all potential target groups have access to e-mail. Respondents have more time to consider their responses.
The primary drawback of e-surveys is twofold at present: There is a lack of comprehensive sampling frames e. It is possible to reach local. Data Relevancy The random variables and the data selected for analysis must be problem specific. Examples include: The respondent is requested to complete the questionnaire and to return it by mail or to hand it in at a specified venue. The right choice of variables must be made to ensure that the statistical analysis addresses the business problem under investigation.
This means that the analyst manipulates certain variables under controlled conditions. This all has an influence on data quality. Guidelines on questionnaire design can be found in marketing research texts and quantitative research methodology texts. Statistical methods called experimental design models are used to analyse experimental data. Experimentation has two main disadvantages: Its design is critical to the success of a study. It must therefore be relevant. Chapter 1 — Statistics in Management The advantages and disadvantages on page 16 apply to any self-administered questionnaire such as those handed out randomly in shopping malls.
Data on the primary variable under study can then be monitored and recorded. The main advantage of data gathered through experimentation is its high quality. All surveys rely upon a questionnaire to structure and record the data collection. The choice of questions as well as their structure. Experimentation Primary data can also be obtained by conducting experiments. As shown in this chapter. Data can be classified by type. Data Enrichment Data can often be made more relevant to the management problem by transforming it into more meaningful measures.
Data quality is influenced by four important factors: Data must be checked for typographic errors. Common terms. The manner in which each data type influences the choice of an appropriate statistical method will be addressed more fully in later chapters.
Managers need to be familiar with the language of statistics if they are to understand reports that contain statistical findings and if they are to interact effectively with statistical analysts.
This chapter also examined data as the raw material of statistics. An understanding of data is useful to assess its quality and hence the validity of the statistical findings on which it is based.
This is known as data enrichment. The inclusion of a few illustrative applications of the use of statistics in management and economics were given to highlight how important it is for managers to have a basic understanding of applied business statistics. When dirty data is used in statistical analysis. Chapter 1 — Statistics in Management Exercises 1 Explain the value of business statistics in management. Over the past six months they had varied both the number of ads placed per week and the advertising media press.
The options were: Does the sample evidence support their claim? Is this a statistic or a parameter? The study aims to describe the profile of performance appraisal systems used by all JSE companies. Name them. Weekly sales volume data was recorded. Scenario 5 Metrorail.
The data from the 25 residential properties sold by their agents. The brief of the researchers was to estimate the percentage of road commuters that converted to train commuting as a result of the campaign. A random sample of commuters was interviewed recently on trains over a period of a week and asked their opinion on issues of personal safety on trains.
Applied Business Statistics c Which random variables are assumed to be related to the variable being predicted? Scenario 1 South Coast Estate Agency wants to determine the average selling price per square metre and size of accommodation of all residential properties in Margate.
KwaZulu- Natal. Scenario 6 Metrorail also recently conducted a campaign to attract road bus. Scenario 2 The owner of the Numbi Restaurant asked a sample of 18 patrons who ate at the restaurant on a particular Saturday evening to complete a short questionnaire to determine their perception of the quality of service and food received that evening.
The results of the sample are to be used to measure the improvement in service. Cape Town conducted a survey during the latest exhibition by randomly selecting visitors as they left the exhibition hall. Also give two illustrative data values for each of these random variables: Chapter 1 — Statistics in Management Scenario 7 The Star newspaper in Gauteng conducted a survey amongst a random cross-section of its subscriber readers to identify the popularity of the various sections of the newspaper amongst all its readers.
How would you rate the service level of your bank? Use the following semantic differential rating scale: Applied Business Statistics 12 Refer to the financial analysis schedule below: Voyager is an SAA customer loyalty programme For each statement Voyager service quality perceptions 9 The following statements relate to your feelings about Voyager services Rank The Voyager Guide Voyager partnership plan Voyager in-flight services Voyager holiday specials Thank you for completing this questionnaire.
Summary Tables and Graphs Outcomes Managers can easily understand sample data when it is summarised into an appropriate table and then displayed graphically. This chapter explains how to summarise data into table format and then how to display the results in an appropriate graph or chart. The choice of a summary table and graphic technique depends on the data type being analysed i. Summary tables and graphs can be used to summarise or profile a single random variable e. A table or a graph can convey information much more quickly and vividly than a written report.
See Excel file C2. Chapter 2 — Summarising Data: Summary Tables and Graphs 2. Table 2. Summary tables and graphs are commonly used to convey statistical results. In practice. The sample dataset in Table 2. Applied Business Statistics 2. A random sample of 30 grocery shoppers was asked to complete a questionnaire that identified: This produces a percentage categorical frequency table. It is always a good idea to express the counts as percentages because this makes them easy to understand and interpret.
Example 2. Convert the counts per category in the third column into percentages of the total sample size. Count and record in the second column the number of occurrences of each category. Then construct vertical bars for each category to the height of its frequency count or percentage on the y-axis. Pie Chart To construct a pie chart. It shows how many times each category appears in a sample of data and measures the relatively importance of the different categories. The size of each segment must be proportional to the count or percentage of its category.
Follow these steps to construct a categorical frequency table: List all the categories of the variable in the first column.
Bar Chart To construct a bar chart. A categorical frequency table can be displayed graphically either as a bar chart or a pie chart. It is only the bar heights that convey the information of category importance. Management Questions 1 Which grocery store is most preferred by shoppers? To construct the percentage frequency table. Summary Tables and Graphs the amount spent last month on grocery purchases their age.
The response data to each question is recorded in Table 2. Then convert the counts into percentages by dividing the count per store by 30 the sample size and multiplying the result by i. Bar charts and pie charts display the same information graphically. The differences between the categories are clearer in a bar chart.
The data source must. Charts and graphs must always be clearly and adequately labelled with headings. A limitation of both the bar chart and the pie chart is that each displays the summarised information on only one variable at a time.
In a bar chart. These joint frequency counts can be converted to percentages for easier interpretation. Sum each row to give row totals per category of the row variable. Sum the column totals or row totals to give the grand total sample size. Follow these steps to construct a cross-tabulation table: Stacked Bar Chart Follow these steps to construct a stacked bar chart: Summary Tables and Graphs Two Categorical Variables Cross-tabulation Table A cross-tabulation table also called a contingency table summarises the joint responses of two categorical variables.
The stacked bar chart can also be constructed by choosing the column variable first and then splitting the bars of the column variable into the category frequencies of the row variable. Sum each column to give column totals per category of the column variable. This produces a simple bar chart of the row variable with each bar split proportionately into the categories of the column variable. The percentages could be expressed in terms of the total sample size percent of total. This summary table is used to examine the association between two categorical measures.
When each pair of data values has been assigned to a cell in the table. Split the height of each bar in proportion to the frequency count of the categories of the column variable. The cross-tabulation table can be displayed graphically either as a stacked bar chart also called a component bar chart or a multiple bar chart. Assign each pair of data values from the two variables to an appropriate category— combination cell in the table by placing a tick in the relevant cell.
Pick n Pay and Spar and then count how many males prefer to shop at each store Checkers. The two charts convey exactly the same information on the association between the two variables. Pick n Pay and Spar. Management Questions 1 How many shoppers are male and prefer to shop at Checkers? Display these categorised simple bar charts next to each other on the same axes. The cross-tabulation table can also be completed using 32 Applied Business Statistics.
They differ only in how they emphasise the relative importance of the categories of the two variables. The multiple bar chart is similar to a stacked bar chart. These joint frequency counts are shown in Table 2. For each category of. Pick n Pay is the most preferred shop 17 shoppers out of 30 prefer Pick n Pay. Summary Tables and Graphs percentages row percentages. Refer to the row percentages in Table 2. Management Interpretation 1 Of the 30 shoppers surveyed.
For males. Refer to the column percentages in Table 2. Applied Business Statistics Table 2. The upper limits are chosen to avoid overlaps between adjacent interval limits. Follow these steps to construct a numeric frequency distribution: Determine the data range. The lower limit for the first interval should be a value smaller than or equal to the minimum data value and should be a number that is easy to use.
From Table 2.
Each interval shows how many numbers data values falls within the interval. The table is known as a numeric frequency distribution and the graph of this table is called a histogram. Single Numeric Variable Numeric Frequency Distribution A numeric frequency distribution summarises numeric data into intervals of equal width. The lower limits for successive intervals are found by adding the interval width to each preceding lower limit.
As a rule. Determine the interval width. Set up the interval limits. Choose the number of intervals. Since the youngest shopper is 23 years old. Assign each data value to one. Tabulate the data values. Histogram A histogram is a graphic display of a numeric frequency distribution. When constructing a numeric frequency distribution. Plot the height of each bar on the y-axis over its corresponding interval.
A count of the data values assigned to each interval produces the summary table. Management Questions 1 How many shoppers are between 20 and 29 years of age? Solution 1 and 2 The numeric and percentage frequency distributions for the ages of grocery shoppers are shown in Table 2.
It shows the proportion or percentage of data values within each interval. The frequency counts can be converted to percentages by dividing each frequency count by the sample size. Follow these steps to construct a histogram: Arrange the intervals consecutively on the x-axis from the lowest interval to the highest. The resultant summary table is called a percentage frequency distribution. There must be no gaps between adjacent interval limits.
This is illustrated in Example 2. Summary Tables and Graphs Table 2. If the numeric data are discrete values in a limited range 5-point rating scales.
Management Questions 1 Which is the most common family size? Construct a numeric and percentage frequency distribution and histogram of the family size of grocery shoppers surveyed. To tally the family sizes. Each family size can be treated as a separate interval. The family sizes range from 1 to 5 see data in Table 2. Cumulative Frequency Distribution Data for a single numeric variable can also be summarised into a cumulative frequency distribution.
Applied Business Statistics Solution Family size is a discrete random variable. For each interval. Summary Tables and Graphs Follow these steps to construct a cumulative frequency distribution: Using the numeric frequency distribution. Ogive An ogive is a graph of a cumulative frequency distribution. This ogive graph can now be used to read off cumulative answers to questions of the following type: How many or what percentage of observations lie below or above this value?
What data value separates the data set at a given cumulative frequency or cumulative percentage? The ogive graph can provide answers for both less than and more than type of questions from the same graph. Plot the frequency count or percentage of zero opposite the upper limit of the extra lower interval. A shortcut method to find each successive cumulative frequency count is to add the current interval frequency count to the cumulative frequency immediately preceding it.
Follow these steps to construct an ogive: On a set of axes. The line graph ends at the sample size. Join these cumulative frequency points to produce a line graph.
For this extra lower interval. On the y-axis. The numeric and percentage frequency distributions are both shown in Table 2. Referring to the upper limits for each successive interval above R Choosing five intervals.
Approximate your answer. Solution 1 The numeric frequency distribution for amount spent is computed using the construction steps outlined earlier. The cumulative frequency count for this interval is zero. Based on the numeric frequency distribution in Table 2. Summary Tables and Graphs The ogives for both the frequency counts and percentages are shown in Table 2.
This means that no shopper spent less than R or more than R2 last month on groceries. Using the percentage cumulative frequency polygon. Plot each pair of data values x. Applied Business Statistics Note: The ogive is a less than cumulative frequency graph. The box plot is covered in Chapter 3. Box Plot A box plot visually displays the profile of a numeric variable by showing its minimum and maximum values and various intermediate descriptive values such as quartiles and medians.
The graphs that are useful to display the relationship between two numeric random variables are: A visual inspection of a scatter plot will show the nature of a relationship between the two variables in terms of its strength the closeness of the points.
Label the vertical axis y-axis with the name of the variable being influenced called the dependent variable. Another example is to examine what influence training hours on the x-axis could have on worker output on the y-axis.
Construct a scatter plot for the amount spent on groceries and the number of visits to the grocery store per shopper by the sample of 30 shoppers surveyed. Follow these steps to construct a scatter plot: Label the horizontal axis x-axis with the name of the influencing variable called the independent variable.
Scatter Plot A scatter plot displays the data points of two numeric variables on an x—y graph. Each graph addresses a different type of management question.
Two Numeric Variables The relationship between two numeric random variables can be examined graphically by plotting their values on a set of axes. Such data is called time series data. The x-variable is time and the y-variable is a numeric measure of interest to a manager such as turnover.
Since the number of visits is assumed to influence the amount spent on groceries in a month. Follow these steps to construct a trendline graph: The horizontal axis x-axis represents the consecutive time periods. The more frequent the visits. Trendline Graph A trendline graph plots the values of a numeric random variable over time. There is only one possible outlier — shopper The consecutive points are joined to form a trendline.
Solution To construct the scatter plot.
The values of the numeric random variable are plotted on the vertical y-axis opposite their time period. The results of the scatter plot are shown in Figure 2. Applied Business Statistics Trendline graphs are commonly used to identify and track trends in time series data. After plotting all 32 y-values. For each week. Management Question By an inspection of the trendline graph.
Solution To plot the trendline. The more unequal the two distributions. A Lorenz curve shows what percentage of one numeric measure such as inventory value. Summary Tables and Graphs Lorenz Curve A Lorenz curve plots the cumulative frequency distributions ogives of two numeric random variables against each other. For each interval of the y-variable.
Derive the cumulative frequency percentages for each of the two distributions above. If the distributions are similar or equal. The two numeric frequency distributions and their respective percentage ogives for the value of savings balances and number of savings accounts are given in Table 2.
It was originally developed by M Lorenz to represent the distribution of income amongst households. Follow these steps to construct a Lorenz curve: Identify intervals similar to a histogram for the y-variable. Calculate the total number of objects e.
The degree of concentration or distortion can be clearly illustrated by a Lorenz curve. Its purpose is to show the degree of inequality between the values of the two variables. Solution Figure 2. Management Question Are there equal proportions of savers across all levels of saving accounts balances? Comment by inspecting the pattern of the Lorenz curve. In this example, an unequal distribution is evident. Overall, this bank has a large number of small savers, and a few large savers.
Its purpose is to identify a possible relationship between the numeric variable and the categorical variable s. For example, the ages of MBA students can be split by the categorical variable gender to determine whether the average age of male and female MBA students is the same or different.
Breakdown analysis is shown in a cross-tabulation table or a pivot table where the rows and columns of the table represent the categorical variables and values inside the table show the descriptive statistic e. In addition, the economic focus i. The results are shown in Table 2. The graph of a breakdown table is either a simple bar chart if the numeric variable is segmented by only one categorical variables or a multiple or stacked bar chart if the numeric variable is split into the different categories of two categorical variables.
By inspection, actively-managed funds perform marginally better, on average, than index-tracking funds. The nature of the relationship is as follows: The best-performing unit trusts are the actively-managed financial funds 8.
The property-focused unit trust funds 7. The industrial- focused funds underperformed by almost 1. Actively-managed funds have outperform index-tracking funds by almost 0.
Other numeric descriptive statistical measures such as minimum, maximum, medians, quartiles, standard deviation, sub-sample sizes, etc. A Pareto curve is a combination of a sorted bar chart and a cumulative categorical frequency table. In a sorted bar chart the categories on the x-axis are placed in decreasing order of frequency or importance. For example, what are the top three causes of machine failure out of a possible 25 causes — and what percentage of failures do they represent?
This allows a manager to focus on the few critical issues and address these issues ahead of the remaining many trivial issues.
Follow these steps to construct a Pareto curve: Construct a categorical frequency table for the categorical random variable. Rearrange the categories in decreasing order of frequency counts or percentages. Calculate the cumulative frequency counts or cumulative percentages starting from the highest frequency category on the left to the lowest frequency category on the right. Plot both the bar chart using the left y-axis for the frequency counts or percentages and the percentage cumulative frequency polygon using the right y-axis on the same x—y axes.
Code Description Count 1 Poor product knowledge 26 2 Product options limited 47 3 Internet site frequently down 12 4 Slow response times 66 5 Unfriendly staff 15 6 Non-reply to queries 22 7 Cost of service is excessive 82 8 Payment options limited 30 Total Use the table to construct a Pareto curve. Management Questions 1 From the Pareto curve, identify the top three customer complaints.
Figure 2. Management Interpretation 1 The top three customer complaints are 7: Cost of service is excessive, 4: Slow response times, and 2: Product options limited identified by the left three bars. The Chart option is used to display these tables graphically. Follow these steps to create a one-way pivot table in Excel Highlight the data range of the categorical variable s to be summarised.
From the menu bar in Excel, select Insert, then select the PivotTable icon. In the Create PivotTable input screen, check that the correct data range is selected. The one-way pivot table is constructed as the variable is dragged to each box in turn. To construct a cross-tabulation table or two-way pivot table , follow the same steps as for a one-way pivot table, but drag one of the categorical variables to the Row Labels box and the other categorical variable to the Column Labels box.
Bar Charts and Pie Charts To construct a chart from a pivot table pie chart, column bar chart, stacked bar chart or multiple bar chart , place the cursor in the pivot table area and select the Insert tab and the Chart option from the menu bar.
Then select the chart type Column, Pie or Bar to display the pivot table graphically. The charts that are produced are the same as those shown in Figure 2. Scatter Plots and Line Graphs For numeric data, the scatter plot and the trendline graphs can be generated by highlighting the data range of the numeric variables to be displayed and selecting the Chart option within the Insert tab in the menu bar. The Scatter chart type will produce the scatter plot for two numeric variables see Figure 2.
The Lorenz curve can be constructed using the Scatter chart type and selecting the option Scatter with Smooth Lines and Markers. The input data would comprise the cumulative percentage ogives for the two numeric random variables being compared. The Data Analysis Add-In Excel offers a data analysis add-in that extends the range of statistical analyses that can be performed to include more advanced statistical techniques. To add this module, follow this sequence in Excel To use any of the statistical tools within the data analysis add-in, select the Data tab and then the Data Analysis option in the Analysis section of the menu bar.
Numeric Frequency Distribution and Histogram The Histogram option within Data Analysis is used to create numeric frequency distributions, histograms, ogives both count and percentages and the Pareto curve. To apply the histogram option, first create a data range consisting of a label heading and the upper limits of each interval in column format.
Excel calls this data range of interval upper limits a Bin Range. In Example 2. Then complete the data input preparation dialog box for the histogram is shown in Figure 2. To produce a numeric frequency distribution and histogram, complete the following inputs: The Input Range defines the dataset include the variable name. The Bin Range defines the data range of upper limits of each interval. Tick the Labels box to indicate that the variable names have been included in each of the Input Range and Bin Range.
Tick the Chart Output box to display the histogram in the output. The output is similar to that shown in Table 2. Note in Figure 2. This is done by ticking the option Pareto sorted histogram and Cumulative Percentage. The categorical frequency table summarises and profiles a single categorical random variable. When two categorical variables are examined simultaneously for a possible association, a cross-tabulation table summarises their joint frequencies.
Charts, such as the pie chart, the simple bar chart, the stacked or component bar chart and the multiple clustered bar chart, are all used to pictorially display categorical data from qualitative random variables.
Applied business statistics: Notify me. Description This text aims to differentiate itself from other business statistics texts in two important ways. It seeks: This further edition continues the theme of using Excel as a computational tool to perform statistical analysis.
While all statistical functions have been adjusted to the Excel format, the statistical output remains unchanged. Summarizing data - location measures 5. Descriptive statistics - location measures 6. Basic probability concepts 8. Probability distributions 9. Confidence interval estimation Chi-Squared hypothesis tests Analysis of variance - comparing multiple population means Index numbers - measuring business activity Time series analysis - a forecasting tool Notes "These worked solutions accompany Wegner: Applied Business Statistics: Methods and Excel-based Applications, Second Edition.
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