Question

63, 40, 40, 39, 56, 45, 48, and 76

a. Find the sample mean

b. Find the sample median

c. Find the sample mode

d. Find the sample range

e. Find the lower and upper quarrtiles, and the sample interquartile range IQR

Q1=

Q3=

IQR=

f. Display the data with a boxplot (with fences and whiskers)

Fences:

g. Write a brief description of this data (symmetry, outliers)

h. Which is the better summary measure of these data, the mean or the median? Explain

i. Find the approximate value of the 85th percentile.

Give a brief interpretation of this precentile

j. If two data sets have the same range:

1. the distanve from the smallest to largest observation are the same in both sets

2. the smallest and largest observation are the same in bothsets

3. both sets will have the same variance

4. both sets will have the same interquartiles range

Answer 1

a) Sample Mean= (63+40+40+39+56+45+48+76)/8=407/8=50.875

b) Acceding order of data is 39,40,40,45,48,56,63,76. Since there are even number of data. So, Median is the average of two middle most data in sorted form. Meadian= (45+48)/2= 93/2= 46.5

c) Write frequency corresponding to each of the number as

data: 39,40,45,48,56,63,76

freq: 1,2,1,1,1,1,1,1

Here the number 40 has maximum frequency & it is equal to 2. So, Mode of data is 2.

d) Sample range= Max-Min

=76-39=37

e) Q1 is that observation about which data contain 25% of the value and Q3 is that observation about which data contain 75% of the value.

So, Q1=40.00 and Q3=57.75
IQR=Q3-Q1=57.75-40.00= 17.75

f)

g) summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
39.00 40.00 46.50 50.88 57.75 76.00

Above Box plot shows that there is no outlier present in the dataset.

h) Median is the better summary measure of the data. Median is the middle value of the data which dived dataset into two parts. For boxplot, the median is used, not mean to show the outlier is present in the dataset or not.