Descriptive Statistics:

Tabular and Graphical Methods

Descriptive Statistics: Tabular and Graphical Methods

Descriptive Statistics are used to condense and summarize data that have been collected. Can be done in three ways:

1. Tables

2. Graphs or figures

3. Statistics: A rule that reduces data to a single number

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Frequency Distribution

• A tabular summary of data showing the frequency (or number) of items in each of several nonoverlapping classes.

• The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.

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Example: President Hotel

• Guests staying at Guest House 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 shown below.

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Conducting R

x <- c("Below Average", "Average", "Above Average", "Above Average", 
       "Above Average", "Above Average", "Above Average", "Below Average", 
       "Below Average", "Average", "Poor", "Poor", "Above Average",
       "Excellent", "Above Average", "Average", "Above Average", 
       "Average", "Above Average", "Average")  
x

##  [1] "Below Average" "Average"       "Above Average" "Above Average"
##  [5] "Above Average" "Above Average" "Above Average" "Below Average"
##  [9] "Below Average" "Average"       "Poor"          "Poor"         
## [13] "Above Average" "Excellent"     "Above Average" "Average"      
## [17] "Above Average" "Average"       "Above Average" "Average"

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table(x)

## x
## Above Average       Average Below Average     Excellent          Poor 
##             9             5             3             1             2

data.frame (table (x))

##               x Freq
## 1 Above Average    9
## 2       Average    5
## 3 Below Average    3
## 4     Excellent    1
## 5          Poor    2

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prop.table(table(x)) ### relative frequency ###

## x
## Above Average       Average Below Average     Excellent          Poor 
##          0.45          0.25          0.15          0.05          0.10

data.frame(prop.table(table(x))) ### relative frequency ###

##               x Freq
## 1 Above Average 0.45
## 2       Average 0.25
## 3 Below Average 0.15
## 4     Excellent 0.05
## 5          Poor 0.10

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round(prop.table(table(x)), 2)

## x
## Above Average       Average Below Average     Excellent          Poor 
##          0.45          0.25          0.15          0.05          0.10

round(100*(prop.table(table(x))))

## x
## Above Average       Average Below Average     Excellent          Poor 
##            45            25            15             5            10

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cumsum(prop.table(table(x)))

## Above Average       Average Below Average     Excellent          Poor 
##          0.45          0.70          0.85          0.90          1.00

data.frame(cumsum(prop.table(table(x)))) ## how about round of this values ##

##               cumsum.prop.table.table.x...
## Above Average                         0.45
## Average                               0.70
## Below Average                         0.85
## Excellent                             0.90
## Poor                                  1.00

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require(COUNT)    ## making myTable ##

## Loading required package: COUNT
## Loading required package: msme
## Loading required package: MASS
## Loading required package: lattice
## Loading required package: sandwich

myTable(x)

##               x Freq Prop CumProp
## 1 Above Average    9 0.45    0.45
## 2       Average    5 0.25    0.70
## 3 Below Average    3 0.15    0.85
## 4     Excellent    1 0.05    0.90
## 5          Poor    2 0.10    1.00

Slide with Plot

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Coool!!, Isn’t it?