mid term examnination business statistic

As aresult, for skewed distributions, the mean is a poor descriptive statistic.● Because this frequency table has 65 missing values, using Mean may produceerroneous results.Advantages: ●

NATIONAL ECONOMICS UNIVERSITY

-*** -MID-TERM EXAMNINATIONBUSINESS STATISTIC

Group 4: 11210447 Mai Le Chau Anh 11215591 Nguyen Quynh Anh 11210899 Nguyen Ba Gia Bach 11211907 Nguyen Ngan Ha 11214285 Dinh Bao Ngoc 11215555 Ta Thi Minh Thu

Class: Advanced International Business Administration 63B

Lecturor: Assoc.Prof Tran Thi Bich

II DATA DESCRIPTION 12

III DESCRIPTIVE STATISTICS 12

IV.ANALYTICAL TECHNIQUES 16

V FINDINGS AND INSIGHTS 16

VI CONCLUSION 17

PART I: QUESTIONS

Question 1: Consider the variable income in gss.sav file (the variable is total family income

in the year before the survey)

1 Make a frequency table for the variable Does the frequency table make sense? Does itmake sense to make a histogram of the variable? A bar chart?

2 What is the scale of measurement for the variablẻ

3 What descriptive statistics are appropriate for describing this variable and why? Doesit make sense to compute a mean?

4 Discuss the advantages and disadvantages of recording income in the manner.Describe other ways of recording income and the problem associated with each ofthem

Question 2: In the gss.sav file, the variable tvhours tells you how many hours per day GSS

respondents say they watch TV.

1 Make a frequency table of the hours of television watched Do any of the values strikeyou as strange? Explain

2 Based on the frequency table, answer the following questions: Of the people whoanswered the question, what percentage don’t watch any television? What percentagewatch two hours or less? Five hours or more? Of the people who watch TV, whatpercentage watch one hour? What percentage watch four hours or less?

3 From the frequency table, estimate the 25th, 50th, 75th, 95th percentiles What is thevalue for the Median, Mode?

4 Make a bar chart of the hours of TV watched What problem do you see with thisdisplay?

5 Make a histogram of the hours of TV watched What causes all of the values to beclumped together? Compare this histogram to the bar chart you generated in question2d Which is a better display for these data?

Question 3:

Find a data set which is related to a specific organizational problem (either at the macro ormicro level) and apply all possible descriptive statistical techniques that you think suitable tothe problem Write a short report, which includes the objectives of your analysis, the researchquestions and your findings The maximum length of the report is 5 pages including Tablesand Figures

PART II: ANSWERSQuestion 1

=> This frequency table makes sense because this frequency table is a Grouped FrequencyTable, and there are so many values in income data, we need a frequency table to accuratelydescribe pay groups Furthermore, all of the frequency, percentage, and cumulativepercentages reflect the family income category in general.

on the histogram's X-axis represent the scale of values within which the measurements fall,while the Y-axis represents the number of times the values occurred inside the intervals Whilean equal width histogram of the income variable is achievable since family income isnormally continuous data with the same class intervals, it is not recommended and so does notmake sense in this circumstance The missing values column is not expressed clearly since itis contained within the non-missing values column, which might lead to manymisconceptions As a result, using the histogram for this variable makes no sense.

BAR CHART

A bar chart is a feasible alternative when displaying a distribution of data points or comparingmetric values We can observe which group has the greatest number or how they compare toother groups using the bar chart Despite the multiple numbers on the X-axis, we can readilydetect the trend and make a conclusion from this bar chart So, in this case using a bar chartmakes sense

1.2

This variable income has an ordinal scale of measurement since it has been separated intovarious categories that are not measured but only labeled Furthermore, the scale ofmeasurement for revenue in the gss.sav file is ordinal.

The yellow row is the variable “income”

Measures of Dispersionor Variation

Measures of Position

- Count, Percent, Frequency- Displays how frequently something occurs

- Use this to display how frequently a response is delivered

- Mean, Median, and Mode

- Locates the distribution by various points- Use this when you want to show how an average or most commonly indicated response

- Range, Variance, Standard Deviation- Identifies the spread of scores by stating intervals

- Range = High/Low points

- Variance or Standard Deviation =difference between observed score and mean- Use this when you want to show how "spread out" the data are It is helpful to know when your data are so spread out that itaffects the mean

- Percentile Ranks, Quartile Ranks- Describes how scores fall in relationto one another Relies on standardized scores- Use this when you need to compare scores to a normalized score (e.g., a national norm)

=> The Measure of Central Tendency (Median and Mode) is most suited for defining thisvariable since it is closer to our goal of determining the most often reported response

Median and Mode rather than Mean:

● We have no information on the values in this range (less than $1,000 and more than$110,000) In this range, the severe courses are available.

● We can observe that the histogram (drawn in part 1.1) is strongly skewed to the rightwhen we draw it and the Coefficient of Skewness is smaller than 0 (negative) As aresult, for skewed distributions, the mean is a poor descriptive statistic.

● Because this frequency table has 65 missing values, using Mean may produceerroneous results.

Advantages:

● It may help in determining the form and spread of income distribution.

● It may help in determining the most common or usual number or range, known as themode.

● It might be useful for comparing income data across several categories, such as gender,age, or occupation.

● It can assist in identifying outliers or extreme income numbers that are much higher orlower than the rest of the data.

Question 2:

2.1.As can be seen from the frequency table below, the figure that stands out to me is 12 which corresponds to the 12 hours a day spent watching television The number of individualswho watch TV from 0 to 10 hours is pretty high, but the data begin to fall precipitously afterthe variable 11 However, only variable 12 is unusually higher in this set of variables rangingfrom 11 to 24, which strikes us as unusual.

-Hours per day watching TVFrequencyPercentValid Percent

CumulativePercent

Of the people who answered the question:

● 6% of the people don’t watch any televisions.

● 53.1% of the people watched TV for two hours or less.

● 16,6% of the people watched TV for five hours or more (100% - (6% = 20,9% +26,3% + 17,5% + 12,7%) = 16,6%)

● 83.4%, which is the total valid percent of whom watching TV from 0 to 4hours (6% + 20,9% + 26,3% + 17,5% + 12,7% = 83,4%

Of the people who watch TV (which means the values of variable is excluded):0

● 20.9% watch TV for one hour

● 82.27% watch TV for four hours or less ( x 100% = 82,27%)● 852 is the total number of people who watch TV (906 – 54 = 852)● 701 is the total number of people who watch TV from 1 to 4 hours per day

(189 + 238 + 159 + 115 = 701)

StatisticsHours per day watching TV

● The value for 75 percentiles is 4.00

● The value for 95 percentiles is 8.00th

● The values for Median 2.00

● The values for Mode is 2

BAR CHART

There are a few problems with this bar chart:

● A few outliers with low frequencies exist, however they can be used in a huge numberof discrete values.

● Some values (9, 13, 16, 17, 18, 19, 21, 22, 23) are missing since they do not occur inthe survey answer The bar chart below lacks a gap that reflects these uncollected data(missing values), which might lead to misinterpretation for readers at first look.

● The real form of the distribution is difficult to determine because there are lowfrequencies indicated for higher classes.

the distribution while the right tail of the distribution is longer), all of the values in thehistogram are grouped together This indicates that most of the survey respondents watchtelevision for between one and four hours, with only a small percentage watching it for morethan 10 hours.

In this situation, we believe a histogram would perform better than a bar chart As wementioned in paragraph (2.4), the bar chart DOES NOT indicate the gap that represents theuncollected data, but the histogram tells a different tale Therefore, since the histogram canboth "show the distributions of the values of data collected" and "show a gap to representthese uncollected data," it would be a superior way to display the data

This study has two core reaseach questions:

1.1 Evaluating Perceptions of HATCO: "How do customers perceive HATCO across variousattributes, including delivery speed, pricing, flexibility in negotiations, manufacturer's image,service quality, salesforce image, and product quality? What are the strengths and areas inneed of improvement according to customer ratings?"

1.2 Examining Purchase Outcomes: "What are the outcomes of customer interactions withHATCO in terms of usage levels and satisfaction levels? How does this data inform HATCO'smarket share within its customer base and overall customer satisfaction?"

2.2.1 HATCO Perceptions (Variables X1 to X7):

These attributes encompass the speed of product delivery (X1), perceived pricing level (X2),willingness to negotiate prices (X3), the overall image of the manufacturer (X4), servicequality (X5), the image of HATCO's salesforce (X6), and product quality (X7).

2.2.2 Purchase Outcomes (Variables X9 and X10):

Two variables capture the outcomes of customer interactions with HATCO:

- X9, "Usage level," quantifies the percentage of a firm's total product purchases made fromHATCO, with values ranging from 0 to 100 percent on a 100-point scale.

- X10, "Satisfaction level," assesses customer satisfaction with prior purchases from HATCOusing a visual rating scale, similar to the one applied to measure perceptions (X1 to X7).

III.DESCRIPTIVE STATISTICS3.1 Perceptions of HATCO

3.1.1 Measures of central tendency (mean, median, mode) and dispersion (range, variance,

standard deviation) for variables X1 to X7:

Statistics

Service SalesforceImage

6 C of S of Salesforce Image = 3* (2.665- 2.6)/ 7709= 0.257 C of S of Product Quality = 3* ( 6.971- 7.150)/ 1.5852= -0.33

3.1.2 Histograms or bar charts to visualize the distribution of perceptions for each attribute

(X1 to X7):

The coefficient of skewness of Delivery Speed Price Level Manufacturer Image, , and

Salesforce Image have a relatively same shape: The distribution is slightly skewed to theright This means that the right tail of the distribution is slightly longer than the left tail A

slightly skewed to the right distribution is still relatively symmetrical

witness the similar shape: The distribution is slightly skewed to the left This means that the

left tail of the distribution is slightly longer than the right tail A slightly skewed to the leftdistribution is still relatively symmetrical It is possible to see this skewness if you look at ahistograms.

3.1.3 Calculate percentiles to understand the distribution of responses for each attribute:

Manufacturer Image

ServiceSalesforce Image

3.2.1 Measures of central tendency (mean, median) and dispersion (variance, standard

deviation) for variables X9 (Usage level) and X10 (Satisfaction level):

Satisfaction Level

From the below result, here we visualize the distribution shapes:

C of S of Usage Level (-0.13) indicates that the distribution is slightly skewed to theleft This means that the left tail of the distribution is slightly longer than the right tail So it isa negative skew A moderately skewed to the left distribution is not perfectly symmetrical.However, it is not as skewed as a severely skewed to the left distribution Similarly, C of S of

3.2.3 Analyze the relationship between satisfaction (X10) and perceptions (X1 to X7) using

scatterplots or correlation coefficients:

Price Level

** Correlation is significant at the 0.01 level (2-tailed).

Overall, the Pearson Correlation technique suggests that there is a very strong

positive correlation between Product Quality and Usage Level; Satisfaction Level and

Price Level; Satisfaction Level and Delivery Speed This means that as the Product Quality

not be perfectly linear In other words, there may be some Product Quality outliers, or there

levels than expected.

- Calculate correlation coefficients (e.g., Pearson) to assess relationships between continuous

variables (e.g., between X1 to X7, X9, and X10).

- Interpret the strength and direction of correlations between variables.

5.1 Perceptions of HATCO

5.1.1 Summarize the central tendencies and distributions of perceptions:

The analysis reveals varying customer perceptions of HATCO across different attributes.Delivery Speed (X1) receives a moderately centered rating, indicating room for consistencyimprovement Price Level (X2) is perceived as relatively lower on the scale, suggesting a needfor pricing strategy enhancement Price Flexibility (X3) garners a moderately positiveperception Manufacturer Image (X4) is positively rated with moderate consistency Service(X5) shows consistent but lower ratings Salesforce Image (X6) indicates a somewhat positiveperception, while Product Quality (X7) is rated moderately positively with some variability.

indicating that customers hold a favorable perception of HATCO's manufacturer image Onthe contrary, Price Level (X2) received the lowest mean rating, suggesting that customersperceive HATCO's pricing as less competitive.

5.1.3 Explore if there are variations in perceptions across different firm characteristics:

The mean perception scores for each attribute were compared between these two groups, andstatistical tests were applied where appropriate to assess the significance of these differences.

For Usage Levels, HATCO may focus on maintaining the balanced distribution and managingthe moderate variability in usage patterns For Satisfaction Levels, it is crucial for HATCO toinvestigate the factors contributing to the negative skew, identify dissatisfied customers'concerns, and develop strategies to improve overall customer satisfaction in a business-to-business context.

5.2.2 Investigate the relationship between satisfaction and perceptions of HATCO.

The relationship between customer satisfaction and various perceptions of HATCO is

complex Manufacturer image has a strong positive correlation with satisfaction, while price

flexibility, service, and product quality have negative correlations Factors like delivery speedand price level show more moderate correlations with satisfaction The findings suggest thatimproving service quality, price flexibility, and product quality might positively impactcustomer satisfaction These insights provide a foundation for further analysis and strategicdecision-making within HATCO to enhance customer satisfaction and improve businessoutcomes.

The higher Product Quality is, the higher Usage Level is The relationship between

Satisfaction Level with Delivery Speed and Price Level also witnessed the same trend.There is a slightly skewed to the right distribution for Delivery Speed Price Level, ,

Manufacturer Imageand Salesforce Image while Price Flexibility, Service and ProductQuality have an inverse shape.