Question

1.   The following data set is the number of hours that a sample of college students

   spent studying for a test:

          0, 0, 0 , 3, 3, 5, 6, 6, 8, 10, 12, 15

a)Find the 5-number summary for this data: Low, Q1.Q2,Q3 High  

  b) Use the 5-number summary to make a box-and-whisker plot for this set of data. Be sure to use a number line with an appropriate scale.

c) Based on the box-and-whisker plot, is the data skewed left, skewed right, or  symmetric?

Answer 1

a)

low value means the minimum value =0

high value means the maximum value which is 15

0, 0, 0 , 3, 3,   5, 6,     6, 8, 10, 12, 15

Q2 means median,so we have to find middle number of this data

middle number =(5+6)/2 =11/2 =5.5

So Q2 =5.5

to find Q1,we take data on the left side of median

0, 0, 0 , 3, 3, 5

now we find middle of this

Q1 =(0+3)/2 =3/2 =1.5

to find Q1,we take data on the right side of median

6, 6, 8, 10, 12, 15

now we find middle of this

Q3 =(8+10)/2 =18/2 =9

b)

The box whisker plot is

c)

from the box plot,it can be seen that most of the data lies on the right side of the median,hence this data is skewed right