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Categorical Data. Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent , above average , average , below average , or poor . The ratings provided by a sample of 20 guests are:. Example: Marada Inn. Above Average Above Average - PowerPoint PPT Presentation

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CHAPTER 2, PART A

Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: Below Average Above Average Above Average Average Above Average Average Above Average Average Above Average Below Average Poor Excellent Above Average Average Above Average Above Average Below Average Poor Above Average AverageExample: Marada Inn 3 9 5 2 1Categorical Data# 1 PoorBelow AverageAverageAbove AverageExcellentRatingFrequencyExample: Marada InnTotal 202359Categorical Data#PoorBelow AverageAverageAbove AverageExcellent 10 15 25 45 5 100 RelativeFrequency PercentFrequencyRatingExample: Marada Inn .051.00.10.15.25.45 1Total 202359FrequencyCategorical Data#PoorBelowAverageAverage AboveAverageExcellentFrequencyRatingCategorical Data12345678910Marada Inn Quality RatingsWhat is the scale of Marada Inn Quality Rating?

Nominal When a variable has nominal scale, the shape of the distribution is meaningless.

When a variable has ordinal scale, the shape of the distribution is important.# BelowAverage 15%Average 25% AboveAverage 45%Poor10%Excellent 5% Marada Inn Quality RatingsCategorical DataINSIGHTS:

One-half of the customers surveyed gave Marada a quality rating of above average or excellent. This might please the manager.

For each customer who gave an excellent rating, there were two customers who gave a rating of poor. This should displease the manager.

#

Pelican StoresPelican Stores is chain of womens apparel stores. It recently ran a promotion in which discount coupons were set to customers of other National Clothing stores. Data collected for a sample of 100 in-store credit card transactions at Pelican Stores during one day while the promotion was running are shown in Table 2.18. Customers who made a purchase using a discount coupon are referred to as promotional customers and customers who made a purchase but did not use a discount coupon are referred to as regular customers. Because the promotional coupons were not set to regular Pelican Stores customers, management considers the sales made to people presenting the promotional coupons as sales it would not otherwise make. Customer 5 purchased 2 items, which cost her $54

Pelican StoresPelican Stores is chain of womens apparel stores. It recently ran a promotion in which discount coupons were set to customers of other National Clothing stores. Data collected for a sample of 100 in-store credit card transactions at Pelican Stores during one day while the promotion was running are shown in Table 2.18. Customers who made a purchase using a discount coupon are referred to as promotional customers and customers who made a purchase but did not use a discount coupon are referred to as regular customers. Because the promotional coupons were not set to regular Pelican Stores customers, management considers the sales made to people presenting the promotional coupons as sales it would not otherwise make.

Pelicans management would like to use this sample data to learn about its customer base and to evaluate the promotion involving discounts.

Managerial ReportUsing graphs and tables, summarize the qualitative variables.

data_pelican.xlsA large majority of the customers use National Clothings proprietary credit card.

The overwhelming majority of customers are female.

Most of the customers are married.#Example: Hudson Auto RepairThe manager of Hudson Auto would like to have better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar.917893577552998097627169728966757975727610474626897105776580109859788688368716967746282981017910579696273Quantitative Data#sorted525762626262656667686868696969717172727374747575757677787979798080828385888991939797979899101104105105109minimummaximumExample: Hudson Auto RepairQuantitative Data#1352576262626265666768686869696971717272737474757575767778797979808082838588899193979797989910110410510510921677 550-5960-6970-7980-8990-99100-109 Cost ($) FrequencyQuantitative DataFrequency distribution

Use between 5 and 20 classes.

Data sets with a larger number of elements usually require a larger number of classes.

Smaller data sets usually require fewer classes.

Class Width = (109 - 52)/6 ~ 10

#2/50.04Relative Freq1.0013/5016/507/507/505/50.26.32.14.14 .104Percent Freq10026321414 10Quantitative Data5050-5960-6970-7980-8990-99100-109 Cost ($) Frequency1321677 5#24681012141618 PartsCost ($)Frequency50 60 70 80 90 100 110Tune-up Parts CostQuantitative Data#

Moderately Skewed LeftSymmetric

Highly Skewed RightQuantitative Data#Ogive for Hudson Auto Repair < 60 < 70 < 80 < 90 < 100< 110Cost ($) CumulativeFrequency 50-59 60-69 70-79 80-89 90-99 100-109 2 13 16 7 7 5Parts Cost ($)Parts Frequency5021531384550Quantitative Dataoh - jive # CumulativeRelativeFrequencyCumulativePercent Frequency 4 30 62 76 90 100 .04.30.62.76.901.00Quantitative DataOgive for Hudson Auto Repair < 60 < 70 < 80 < 90 < 100< 110Cost ($) CumulativeFrequency21531384550# PartsCost ($)20406080100Cumulative Percent Frequency50 60 70 80 90 100 110($90, 76%)Tune-up Parts CostExample: Hudson Auto Repair($50, 0%)($60, 4%)($70, 30%)($80, 62%)($100, 90%)($110, 100%)Quantitative Data#

Pelican Stores -- continued Pelican Stores is chain of womens apparel stores. It recently ran a promotion in which discount coupons were set to customers of other National Clothing stores. Data collected for a sample of 100 in-store credit card transactions at Pelican Stores during one day while the promotion was running are shown in Table 2.18. Customers who made a purchase using a discount coupon are referred to as promotional customers and customers who made a purchase but did not use a discount coupon are referred to as regular customers. Because the promotional coupons were not set to regular Pelican Stores customers, management considers the sales made to people presenting the promotional coupons as sales it would not otherwise make.

Pelicans management would like to use this sample data to learn about its customer base and to evaluate the promotion involving discounts.

Managerial ReportUsing graphs and tables, summarize the qualitative variables.Using graphs and tables, summarize the quantitative variables.data_pelican.xlsOver half of the customers purchase 1 or 2 items, but a few make numerous purchases.

The percent frequency distribution of net sales shows that 61% of the customers spent $50 or more.

Customers are distributed across all adult age groups.#Summarizing Two variablesFinger Lakes Homes.xlsExample:18 6 19 12553010012 14 16 3Quantitative variablequalitative variable45203515PriceRange Colonial Log Split A-FrameTotal< $99,000> $99,000Total Home StyleThe number of Finger Lakes homes sold for eachstyle and price for the past two years is shown below.

#PriceRange Colonial Log Split A-FrameTotal< $99,000> $99,00018 6 19 125530Total10012 14 16 3 Home Style45203515Summarizing Two variablesFinger Lakes Homes.xlsExample:#PriceRange Colonial Log Split A-FrameTotal< $99,000> $99,000 Home StylePriceRange Colonial Log Split A-FrameTotal< $99,000> $99,00018 6 19 125530Total10012 14 16 3 Home Style452035150.32731.00000.10910.34550.21820.26671.00000.31110.35560.0667Summarizing Two variables#PriceRange Colonial Log Split A-FrameTotal< $99,000> $99,000 Home StylePriceRange Colonial Log Split A-Frame< $99,000> $99,00018 6 19 1230Total12 14 16 3 Home Style2035150.60001.00000.40000.301.00000.700.54291.00000.45710.80001.00000.2000Summarizing Two variables#Summarizing Two variablesAdmittedDeniedTotalMale373847048442Female149428274321Total5232753112763AdmittedDeniedTotalMale0.29290.36860.6614Female0.11710.22150.3386Total0.40990.59011.0000Dividing all of the frequencies above by the number of observations yields what the joint probability table below The crosstabulation for the aggregated UC-Berkley data isMale acceptance rate is higher when data is aggregated.Simpsons Paradox Example:

In the Fall of 1973, an observational study on possible gender bias was conducted at UC-Berkeley.

There were 12,763 applicants for graduate admission, of whom 8442 were male and 4321 were female.

Of the male applicants, 3738 were admitted, whereas of the female applicants only 1494 were admitted. #FemaleAdmittedDeniedTotalA8919108B17825Total10627133MaleAdmittedDeniedTotalA512313825B313207520Total8255201345FemaleAdmittedDeniedTotalA0.82410.17591.0000B0.68000.32001.0000MaleAdmittedDeniedTotalA0.62060.37941.0000B0.60190.39811.0000Compute the row percentages to show the Simpsons ParadoxSummarizing Two variablesdata_simpson.xlsAt UC-Berkeley graduate admission decisions are made at the department level.

In 1973, UC-Berkeley had 101 different graduate departments.

For simplicity, we look at only the 2 largest departments.

The tables represent the top two departments (A and B).

#A Negative RelationshipxyQBigMacsPBigMacs0.50215.002Summarizing Two variables#No Apparent Relationshi

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