Question

SHOW ALL WORK

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.

Answer 1

I have used R for determining the results. First I shall put the results, after that, I shall attach the R code. So let's start.

a.

mean = 1.889

median = 2.120

mode = 2.215

range = [0.85, 2.99]

Variance = 0.4870

standard deviation = 0.69791

b. Histogram of the distribution

The entire construction will be elaborated in the code section.

Comment on the shape:

For this, I have calculated another plot, which is the kernel density plot. Here from that plot, I am seeing that the distribution is bimodal, though the global mode exists at the mentioned point. Now the distribution is NOT symmetric, Rather it is slightly negatively skewed.

Code Section:

# Data
install.packages("goeveg")
library(goeveg)
x = c(2.45,2.25,1.42,1.99,1.20,2.09,2.36,2.38,0.85,2.99,2.15,0.85,1.33,1.00,2.85,2.22,2.25,0.88,1.52,2.75)
min(x)
max(x)
# Adjust the breaks accordingly

# Analysis
length(x)
range(x)

byvar = (max(x)-min(x)+1)/10

breaks = seq(0.80,3.00,by = byvar)

# Frequency Distribution
x.cut = cut(x,breaks,right = F)
x.freq = cbind(table(x.cut))

# Various summary measures
summary(x)
sd(x)
cv(x)
mean(x)
var(x)

# OUTPUTs
x.freq

# Histogram

hist = hist(x,breaks = breaks)

# Kernel density plot
plot(density(x))

Hope this answer has helped you. Do let me know in the comment section if you have any question.

Thanks !!