Chapter ISG, Problem 10.1.3P

a.

To determine

To find whether either contain outlier and calculate mean and standard deviation after removing outlier.

Answer to Problem 10.1.3P

Season 1

Outlier=1.78

Mean=1.65

SD=0.078

Season 2

No outlier found

Explanation of Solution

Given information:

  

  

Formula used:

  

  

Calculation:

Season 1

Ordered data set

1.45, 1.57, 1.63, 1.66, 1.66, 1.66, 1.69, 1.69, 1.69, 1.72, 1.72, 1.78

Minimum=1.45

First quartile: 1.45, 1.57, 1.63, 1.66, 1.66, 1.66

n=6

n is number of frequencies

n is even

Middle terms are 1.63, 1.66

  

Median

n=12

n is number of frequencies

n is even

Middle terms are 1.66, 1.69

  

Third quartile: 1.69, 1.69, 1.69, 1.72, 1.72, 1.78

n=6

n is number of frequencies

n is even

Middle terms are 1.69, 1.72

  

Maximum=1.78

IQR=1.705-1.645=0.06

So, 1.5 IQR=1.5(0.06)=0.09

To determine if there are outlier.

Consider the number that are 1.5 IQR

Q₁-1.5 IQR=1.645-0.09=1.555

Q₃+1.5 IQR=1.705+0.09=1.714

Since 1.78 is outside the interval 1.555 to 1.714

Yes season 1 having outlier

Then, 1.78 is the outlier in this data.

Table

  

  18.15

n=12

Using mean formula

  

On solving,

mean=1.65

  

n-1=11

Using SD formula

  

On solving,

SD=0.078

Season 2

Ordered data set

1.54, 1.57, 1.59, 1.60, 1.61, 1.62, 1.63, 1.68, 1.70, 1.71, 1.73, 1.76

Minimum=1.54

First quartile: 1.54, 1.57, 1.59, 1.60, 1.61, 1.62

n=6

n is number of frequencies

n is even

Middle terms are 1.59, 1.60

  

Median

n=12

n is number of frequencies

n is even

Middle terms are 1.62, 1.63

  

Third quartile: 1.63, 1.68, 1.70, 1.71, 1.73, 1.76

n=6

n is number of frequencies

n is even

Middle terms are 1.70, 1.71

  

Maximum=1.78

IQR=1.705-1.585=0.12

So, 1.5 IQR=1.5(0.12)=0.18

To determine if there are outlier.

Consider the number that are 1.5 IQR

Q₁-1.5 IQR=1.585-0.18=1.405

Q₃+1.5 IQR=1.705+0.18=1.885

Since no outlier found

b.

To determine

To explain which season of M is better after removing outlier.

Answer to Problem 10.1.3P

Season 1

Explanation of Solution

Given information:

  

  

Mean of season 1=1.65

Mean of season 2=1.645

Season one was M's better season because outlier removal produce stability in season.