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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.
Wegner, Trevor. Physical Description p. Published Cape Town: Juta, Language English. Check copyright status Cite this Title Applied business statistics: Also Titled Solutions manual. Author Wegner, Trevor. Edition 2nd ed. Subjects Commercial statistics. Contents 1. Setting the statistical scene 2. Using Excel for statistical analysis 4. Summarizing data - location measures 5. Descriptive statistics - location measures 6.
Basic probability concepts 8. Probability distributions 9. 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. Continuous data is any number that can occur in an interval. For example, the assembly time for a part can be between 27minutes and 31minutes e. Measurement Scales Data can also be classified in terms of its scale of measurement.
This indicates the strength of the data in terms of how much arithmetic manipulation on the data is possible. There are four types of measurement scales: nominal, ordinal, interval and ratio. The scale also determines which statistical methods are appropriate to use on the data to produce valid statistical results. Chapter 1 Statistics in Management Nominal data Nominal data is associated with categorical data. If all the categories of a qualitative random variable are of equal importance, then this categorical data is termed nominal-scaled.
Nominal data is the weakest form of data to analyse since the codes assigned to the various categories have no numerical properties. Nominal data can only be counted or tabulated. This limits the range of statistical methods that can be applied to nominal-scaled data to only a few techniques.
Ordinal data is also associated with categorical data, but has an implied ranking between the different categories of the qualitative random variable. Each consecutive category possesses either more or less than the previous category of a given characteristic. Rank ordinal data is stronger than nominal data because the data possesses the numeric property of order but the distances between the ranks are not equal.
It is therefore still numerically weak data, but it can be analysed by more statistical methods i. Interval data Interval data is associated with numeric data and quantitative random variables. Applied Business Statistics The multiple bar chart places more emphasis on the gender differences between stores.
Management Interpretation 1 Of the 30 shoppers surveyed. For males. Since the youngest shopper is 23 years old. The lower limits for successive intervals are found by adding the interval width to each preceding lower limit. 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. As a rule. Refer to the row percentages in Table 2. Follow these steps to construct a numeric frequency distribution: Determine the data range.
Choose the number of intervals. Each interval shows how many numbers data values falls within the interval.
From Table 2. Refer to the column percentages in Table 2. 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 upper limits are chosen to avoid overlaps between adjacent interval limits. Determine the interval width.
Set up the interval limits. Histogram A histogram is a graphic display of a numeric frequency distribution. A count of the data values assigned to each interval produces the summary table.
Plot the height of each bar on the y-axis over its corresponding interval. Tabulate the data values. Assign each data value to one. There must be no gaps between adjacent interval limits. The resultant summary table is called a percentage frequency distribution.
Applied Business Statistics : Methods and Excel-based Applications
When constructing a numeric frequency distribution. Follow these steps to construct a histogram: Arrange the intervals consecutively on the x-axis from the lowest interval to the highest.
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. Summary Tables and Graphs Management Questions 1 2 3 4 How many shoppers are between 20 and 29 years of age? What is the most frequent age interval of shoppers surveyed?
What percentage of shoppers belong to the most frequent age interval? What percentage of shoppers surveyed are 60 years or older? Solution 1 and 2 The numeric and percentage frequency distributions for the ages of grocery shoppers are shown in Table 2. The most frequent age interval is between 30 and 39 years.
If the numeric data are discrete values in a limited range 5-point rating scales. Each family size can be treated as a separate interval. This is illustrated in Example 2.
Management Questions 1 Which is the most common family size? Solution Family size is a discrete random variable. To tally the family sizes. Construct a numeric and percentage frequency distribution and histogram of the family size of grocery shoppers surveyed.
The family sizes range from 1 to 5 see data in Table 2. On the y-axis. Ogive An ogive is a graph of a cumulative frequency distribution. For this extra lower interval. Join these cumulative frequency points to produce a line graph. For each interval. Summary Tables and Graphs Management Interpretation 1 The most common family size of grocery shoppers is two. The line graph ends at the sample size. Plot the frequency count or percentage of zero opposite the upper limit of the extra lower interval.
Follow these steps to construct an ogive: On a set of axes. 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?
Cumulative Frequency Distribution Data for a single numeric variable can also be summarised into a cumulative frequency distribution. Follow these steps to construct a cumulative frequency distribution: Using the numeric frequency distribution. 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.
Approximate your answer. Choosing five intervals. Applied Business Statistics Note: The ogive graph can provide answers for both less than and more than type of questions from the same graph. The numeric and percentage frequency distributions are both shown in Table 2.
Solution 1 The numeric frequency distribution for amount spent is computed using the construction steps outlined earlier. This means that no shopper spent less than R or more than R2 last month on groceries.
The ogives for both the frequency counts and percentages are shown in Table 2. Referring to the upper limits for each successive interval above R The cumulative frequency count for this interval is zero. Summary Tables and Graphs Based on the numeric frequency distribution in Table 2.
Using the percentage cumulative frequency polygon. Another example is to examine what influence training hours on the x-axis could have on worker output on the y-axis.
Two Numeric Variables The relationship between two numeric random variables can be examined graphically by plotting their values on a set of axes. The ogive is a less than cumulative frequency graph. 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.
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.
The box plot is covered in Chapter 3. Since the number of visits is assumed to influence the amount spent on groceries in a month. Management Questions By inspection of the scatter plot. Solution To construct the scatter plot. Summary Tables and Graphs 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.
The results of the scatter plot are shown in Figure 2. Plot each pair of data values x. 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. After plotting all 32 y-values. For each week. Management Question By an inspection of the trendline graph. Trendline graphs are commonly used to identify and track trends in time series data.
Trendline Graph A trendline graph plots the values of a numeric random variable over time. There is only one possible outlier — shopper Follow these steps to construct a trendline graph: The horizontal axis x-axis represents the consecutive time periods. See Excel file C.
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. Solution To plot the trendline. The more frequent the visits. The values of the numeric random variable are plotted on the vertical y-axis opposite their time period. The consecutive points are joined to form a trendline. Lorenz Curve A Lorenz curve plots the cumulative frequency distributions ogives of two numeric random variables against each other.
Follow these steps to construct a Lorenz curve: Identify intervals similar to a histogram for the y-variable. A Lorenz curve shows what percentage of one numeric measure such as inventory value.
The degree of concentration or distortion can be clearly illustrated by a Lorenz curve.
Applied Business Statistics, Methods and Excel-based Applications.pdf
It was originally developed by M Lorenz to represent the distribution of income amongst households. Its purpose is to show the degree of inequality between the values of the two variables. Summary Tables and Graphs Number of workers absent 80 60 40 20 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Weeks Figure 2.
Derive the cumulative frequency percentages for each of the two distributions above. 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.
For each interval of the y-variable. If the distributions are similar or equal.
Calculate the total number of objects e. Management Question Are there equal proportions of savers across all levels of saving accounts balances? Comment by inspecting the pattern of the Lorenz curve. The more unequal the two distributions.
A Pareto curve is a combination of a sorted bar chart and a cumulative categorical frequency table. 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. In a sorted bar chart the categories on the x-axis are placed in decreasing order of frequency or importance.
At the top end of the Lorenz curve. Summary Tables and Graphs Solution Figure 2. 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. In this example. As a tool in quality management. 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. This allows a manager to focus on the few critical issues and address these issues ahead of the remaining many trivial issues. Applied Business Statistics Example 2. Management Questions 1 From the Pareto curve. Cost of service is excessive. Product options limited identified by the left three bars. In the Create PivotTable input screen. Summary Tables and Graphs Figure 2. Slow response times.
Internet site frequently down. Follow these steps to create a one-way pivot table in Excel Highlight the data range of the categorical variable s to be summarised. The Chart option is used to display these tables graphically. From the menu bar in Excel. The one-way pivot table is constructed as the variable is dragged to each box in turn. Figure 2. If not.
To illustrate. To use any of the statistical tools within the data analysis add-in.
Applied Business Statistics, Methods and Excel-based Applications.pdf
Then select the chart type Column. 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. The Lorenz curve can be constructed using the Scatter chart type and selecting the option Scatter with Smooth Lines and Markers.
At the Manage option. The charts that are produced are the same as those shown in Figure 2. Pie or Bar to display the pivot table graphically. The Scatter chart type will produce the scatter plot for two numeric variables see Figure 2. Scatter Plots and Line Graphs For numeric data. The input data would comprise the cumulative percentage ogives for the two numeric random variables being compared.
To add this module. Tick the Labels box to indicate that the variable names have been included in each of the Input Range and Bin Range. Applied Business Statistics Figure 2. Excel calls this data range of interval upper limits a Bin Range. The Input Range defines the dataset include the variable name. To apply the histogram option. In Example 2. The Bin Range defines the data range of upper limits of each interval.
Then complete the data input preparation dialog box for the histogram is shown in Figure 2. In conclusion. Other graphical forms are the line graph which is used to display time series data. This chapter also introduced Excel to create summary tables pivot tables and display them graphically using the various chart options. When the relationship between two numeric random variables is being explored. Note in Figure 2. The output is similar to that shown in Table 2.
Numeric random variables are summarised into numeric frequency distributions. The Pareto curve was introduced as a sorted bar chart to highlight the role of bar charts. This is done by ticking the option Pareto sorted histogram and Cumulative Percentage. When two categorical variables are examined simultaneously for a possible association.
The categorical frequency table summarises and profiles a single categorical random variable. A graphical representation promotes more rapid assimilation of the information to be conveyed than written reports and tables. All computational exercises can be performed either manually or by using Excel.
Show the frequency table in percentage terms C or D of 40 clerical employees are as follows: What percentage of employees are in job grade D? Show the percentage frequency table as a pie chart and as a bar chart. D and E. Rental R a Construct a numerical frequency distribution of office rentals by using the classes: Each person was asked to Summary Tables and Graphs 9 X2. The results are given below.
Applied Business Statistics indicate which fruit juice by the alphabetic label they most preferred. Manufacturer First half Second half Annual sales Toyota 42 54 96 Nissan 35 27 63 Volkswagen 45 42 88 Delta 26 36 62 Ford 32 41 74 MBSA 19 17 37 BMW 24 51 MMI 14 11 25 a Construct a multiple bar chart showing the number of new car sales by manufacturer between the first and the second half of last year. The data is as follows: Summary Tables and Graphs 13 X2. A random sample of 48 estate agents was selected and the number of houses each sold during this period was recorded.
Applied Business Statistics a Construct a frequency count table to show the sales performance of the sample of East London estate agents. Set a bin range to each discrete value of 3.
Since the numeric data is discrete and in a limited data range. Summary Tables and Graphs 18 X2. Use the discrete values as bins. The following data was recorded: Sixty cars were randomly selected at an entry point into the CBD and the number of occupants was noted. Justify your answer. Refer to the Excel file X2. Briefly explain your answer.
In what way? Explain briefly. The analyst wants to know if leverage influences profit growth. Also set the minimum scale on the x-axis to Numeric Descriptive Statistics Outcomes Summary tables pivot tables and graphs provide a broad overview of the profile of random variables. These statistics identify the location. In this chapter they will be explained and the conditions under which each would be appropriate to describe sample data will also be reviewed.
These are provided by a set of numeric measures called descriptive statistics. Dispersion refers to the extent to which the data values are spread about the central location value. Managers and management reports often make statements containing phrases such as: Three characteristics are commonly used to describe the data profile of a random variable.
Three commonly used central location statistics are: These are: Chapter 3 — Describing Data: Numeric Descriptive Statistics 3. They are called central location statistics. All three measures mean. The average daily sales are a measure of central location. These statements all refer to a typical or central data value used to represent where the majority of data values lie. Location refers to the where the data values are concentrated.
This is the purpose of numeric descriptive statistics. The arithmetic mean can only be applied to numeric i. It is not appropriate for categorical i. It uses all the data values in its calculation.
Table 3. An outlier is an extreme value in a data set. It is an unbiased statistic meaning that. The arithmetic mean. What is the average number of training days attended by these financial advisors? These two properties make it the most widely used measure of central location. It is distorted by outliers. It is found by adding up all the data values and then dividing the total by the sample size as shown in the following formula: The arithmetic mean has the following two advantages.
Two alternative central location measures are the median and the mode. Example 3.
Thus the median monthly car sales is 34 cars. Median The median Me is the middle number of an ordered set of data. Follow these steps to calculate the median for ungrouped raw numeric data: Arrange the n data values in ascending order.
It divides an ordered set of data values into two equal halves i. Numeric Descriptive 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: Arithmetic approach — Based on the sample size.
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 data is summarised in the numeric frequency distribution and ogive as shown in Table 3.
The median has one major advantage over the mean — it is not affected by outliers. An approximate median delivery time for parcels is therefore 35 minutes the interval midpoint. For large samples of discrete or categorical nominal and ordinal-scaled data: The most common family size is four.
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. The majority of machine breakdowns last between 25 and 30 minutes. Thus a median. Mode The mode Mo is defined as the most frequently occurring value in a set data.
It makes no sense. It is therefore a more representative measure of central location than the mean when significant outliers occur in a set of data. Numeric Descriptive Statistics Find the median delivery time of parcels to clients by this courier company. This identifies the median interval. Follow these steps to calculate the mode: For small samples of ungrouped data.
It can be calculated both for categorical data and numeric data. A drawback of the median. The supermarket frequented most often in Kimberley is Checkers.
This means that half the deliveries occurred within Applied Business Statistics For large samples of continuous. 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. The midpoint of 35 minutes can be used as an approximate modal courier delivery time. Data type If the data type is categorical nominal or ordinal scaled.
The choice depends mainly on a the data type of the random variable being analysed and b whether outliers are present or not in the data set. If the data type is numeric.
Outliers Outliers distort the mean but do not affect the median or the mode. If the data type is categorical. The mode has several advantages: It is a valid measure of central location for all data types i.
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. If the shape is bi-modal. In such cases. Numeric Descriptive Statistics To calculate a more representative modal value. Which central location measure is best? A central location measure must be representative of its data values. The mode is not influenced by outliers. Follow these steps to calculate the geometric mean: Multiply all n observations which are percentage changes.
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. When each data value is calculated from a different base. Find the average annual percentage increase in the electricity tariff. For example.. The average weekly percentage change in the share price can be found using the geometric mean.
R30 at the end of Week 2 and R33 at the end of Week 3. The formula for the geometric mean GM is as follows: Geometric Mean The geometric mean is used to find the average of percentage change data. Take the nth root of the product. The lower quartile. The upper quartile. Follow these steps to calculate the weighted arithmetic mean based on a numeric frequency distribution: Each observation. R and R respectively cannot simply be averaged. R per hour for a second training programme of six hours and R for a two-hour seminar.
These weighted observations are then summed. It divides an ordered data set into two equal halves. Numeric Descriptive Statistics 1 The arithmetic mean assumes that each data value is equally weighted i. The middle quartile. This sum is then divided by the sum of the weights. Solution Since the duration of each programme differs i.
In formula terms. The weighted arithmetic mean must be applied. Follow these steps to calculate quartiles lower. Upper limit R14 The maximum salary paid for the job grade is R14 per month.
Applied Business Statistics Figure 3. Each quartile position is determined as follows regardless of whether n is even or odd: For a given job grade. 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. Sort the data in ascending order. If the quartile position in not an integer. Quartiles are calculated in a similar way to the median. Thus Q3 is found in the th Solution a The sorted daily electricity consumption values in ascending order are shown in Table 3.
Using Formula 3. Numeric Descriptive Statistics In formula terms: This is the approximate Q3 value. This is the approximate Q1 value. Applied Business Statistics — The fractional part of the upper quartile position is 0. All other terms are identical to those of the median formula. The formula is modified to identify either the lower or the upper quartile position.She randomly samples employees, of whom 96 are female and are male.
What is that percentage of income value? A useful acronym to keep in mind is GIGO, which stands for garbage in, garbage out.
The x-variable is time and the y-variable is a numeric measure of interest to a manager such as turnover. Solution This problem can be represented in a probability tree as shown in Figure 4. Rank ordinal data is stronger than nominal data because the data possesses the numeric property of order but the distances between the ranks are not equal.
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