Skewness :

1) A skewed distribution will have one tail longer than another. Since the shape is asymmetrical, the mean, median and mode are away from each other.

There are two types of skewed distribution:

  1. Left skew distribution or negatively skewed.
  2. Right skew distribution or positively skewed.

Left skew distributions is also known as negatively skewed distribution. This type of distribution has a long left tail. In left skew distribution mode > median > mean.

Histogram:


Right skew distribution also known as positively skewed distribution.

Here, Mode < Median < Mean

Histogram:


2) Sample of 26 offshore oil workers took part in simulated excape exercise, resulting in the accompanying data on time (sec) to complete the escape :

      

A) Construct a stem-and-leaf display of the data.(Enter numbers from smallest to largest separated by spaces.Enter NONE for stems with no values.)


   

How does it suggest that the sample mean and median will compapre?

Ans.
      

The display is reasonably symmetric, so the mean and median will be close.

B) calculate the values of the sample mean x̄ and median x̃.[Hint: Σxj= 9618.](Round your answerw to two decimal places.)

   
Ans.

   mean = 369.92
   median = 369.5

C) By how much could the largest time, currently 421, be increased without affecting the value of the sample median ? (Enter ∝ if there is no limit to the amount.)
 By how much could this value be decreased without affecting the value of the sample median ? (Enter ∝ if there is no limit to the amount.)

Ans.

Infinity, One can increase the value to infinity which will not affect the median.
Infinity, One can also decrease the value to infinty without affecting the median.

D) What are the values of x̄ and x̃ when the observations are reexpressed in minutes? (Round your answers to two decimal places.)

   
Ans.
   x-bar = 6.09
   x-median = 6.16