Question

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1) The following is a list of prices (in dollars) of birthday cards found in various drug stores:

2.45

1.20

0.85

1.33

2.25

2.25

2.09

2.99

1.00

0.88

1.42

2.36

2.15

2.85

1.52

1.99

2.38

0.85

2.22

2.75

a. Using R find the mean, median, mode, range, variance and standard deviation of the data. Attach your output from Excel/R.

b. Using /R, construct a frequency histogram of the data set. Use the guidelines in the class notes. Provide all the details (interval, width, etc.) on how you constructed the histogram. Make sure that you attach the histogram created by Excel/R. Comment on the shape of the frequency distribution (e.g., is the distribution skewed? Is the distribution approximately mound-shaped and symmetric?) for the data set based on your histogram.

c. Based on the results in part a, construct the intervals and for the data set. Be sure to show your interval below. Based on the results in part b what percentage of the measurements for the data set falls in each interval

Answer 1

#a. Using R find the mean, median, mode, range, variance and standard deviation of the data.

prices <- c(2.45, 1.20, 0.85, 1.33, 2.25, 2.25, 2.09, 2.99, 1.00, 0.88,
1.42, 2.36, 2.15, 2.85, 1.52, 1.99, 2.38, 0.85, 2.22, 2.75)

  
Mean <- mean( prices )

Median <- median( prices )
  
findmode <- function(v) {
uniqv <- unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}
  
Mode <- findmode(prices)
  
Range <- range( prices )
Variance <- round( var( prices ) , 3)
StandardDeviation <- round( sd( prices ), 3 )
  

#the mean, median, mode, range, variance and standard deviation of the data
print(Mean)
print(Median)
print(Mode)
print(Range)
print(Variance)
print(StandardDeviation )

#b. Using /R, construct a frequency histogram of the data set. Use the guidelines in the
#class notes. Provide all the details (interval, width, etc.) on how you constructed the
#histogram. Make sure that you attach the histogram created by Excel/R. Comment on the shape
#of the frequency distribution (e.g., is the distribution skewed? Is the distribution
#approximately mound-shaped and symmetric?) for the data set based on your histogram.

#Count the number of data points
length(prices)

#Calculate the number of bins by taking the square root of the number
#of data points and round up.
bins = ceiling(sqrt(length(prices)))
bins

#Calculate the bin width by dividing the specification tolerance or
#range (USL-LSL or Max-Min value) by the # of bins
width = range( prices)/ bins
width

hist( prices, breaks = 5, main = 'Histogram of prices')
# distribution is not mount shaped. It is skewed.

#c. Based on the results in part a, construct the intervals and for the data set.
#Be sure to show your interval below. Based on the results in part b what percentage
#of the measurements for the data set falls in each interval

factors <- factor(cut(prices, breaks=nclass.Sturges(prices)))
#Tabulate and turn into data.frame
out <- as.data.frame(table(factors))
#Add cumFreq and proportions
out <- transform(out, percentage = prop.table(Freq))
out