Question

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

create CSV file and export the data to create histogram.

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

R Code :

summary(X)

Range = max(X)-min(X)

Range

sd= sd(X)
sd

var(X)

Result :

 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.850   1.298   2.120   1.889   2.365   2.990 
[1] 2.14   #Range
[1] 0.6979059  #SD
[1] 0.4870726  #Variance 

B. Code :

Histogram= hist(X)

OUtput :

Here we have taken 5 intervals for 20 observation. Width 0.5 . The distribution is not symmetric. It's negatively skewed.  

C . From part a we got min and max to be 0.85 and 2.99

hence 2.99-0.85=2.04 , so we take lower limit as 0.5 and upper as 3.

so if we split in 5 intervals we will get 0.5 width for each

below is the frequency table :

R code :

low_val =0.5
hi_val= 3
x_break=0.5
breaks=seq(low_val,hi_val,x_break)
breaks

y=cut(X,breaks)
y
z=table(y)
z

Output :

# The breaks :

X_break=

[1] 0.5 1.0 1.5 2.0 2.5 3.0

Y= 
 [1] (2,2.5] (1,1.5] (0.5,1] (1,1.5] (2,2.5] (2,2.5] (2,2.5] (2.5,3] (0.5,1]
[10] (0.5,1] (1,1.5] (2,2.5] (2,2.5] (2.5,3] (1.5,2] (1.5,2] (2,2.5] (0.5,1]
[19] (2,2.5] (2.5,3]
Levels: (0.5,1] (1,1.5] (1.5,2] (2,2.5] (2.5,3]


The frequency table : 
Z 
(0.5,1] (1,1.5] (1.5,2] (2,2.5] (2.5,3] 
      4       3       2       8       3 

that is

Value freq

0.5-1 4

1- 1.5 3

1.5-2 2

2-2.5 8

2.5-3 3

based on part b :

0.5-1 = 4/20=20%

.1-1.5 = 3/20 = 15%

1.5-2=2/20=10%

2-2.5= 8/20=40%

2.5-3= 3/20=15%