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which is true statement based on the dot plots below? A) set b has the greater mean. B) set b has the greater median C) Set a is less symmetric than set b. D) set b has the greater range

which is true statement based on the dot plots below A set b has the greater mean B set b has the greater median C Set a is less symmetric than set b D set b ha class=

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Answer:

The statement which is true about the dot plot is:

        D)    set B has the greater range.

Step-by-step explanation:

Set A--

  • We see that set A is slightly symmetric about the data point 40.
  • Hence, the median of the set is: 40
  • Also, the mean is calculated as follows:

      [tex]Mean=\dfrac{20\times 2+30\times 2+40\times 5+50\times 2+60\times 3}{14}\\\\\\Mean=\dfrac{40+60+200+100+180}{14}\\\\\\Mean=\dfrac{580}{14}\\\\\\Mean=41.42857[/tex]

  • Least value of set= 20

       and Maximum value=60

         Hence, Range= Maximum value-Least value

            i.e. Range= 60-20

                  Range= 40

Set B--

  • Set B is less symmetric

and there are total 16 data points

  • and the median of data is: 30.
  • Also, the mean is calculated as follows:

[tex]Mean=\dfrac{10\times 2+20\times 4+30\times 4+40+50\times 2+60}{14}\\\\\\Mean=\dfrac{420}{14}\\\\\\Mean=30[/tex]

  • Minimum value or least value= 10

                 and Maximum value= 60

               Hence, Range= 60-10

                  Range= 50

Set B has less mean as compared to set A

( Hence, option: A is incorrect)

Also, the median of set B is less than the median of set A.

( Hence, option: B is incorrect)

Also, set A is more symmetric than set B.

( Hence, option: C is incorrect)

Set B has greater range than set A

( since Range of set B=50

and Range of set A= 40 )

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