Question

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

Answer 1

The statement which is true about the dot plot is:

D) set B has the greater range.

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:

`Mean=(20* 2+30* 2+40* 5+50* 2+60* 3)/(14)\\\\\\Mean=(40+60+200+100+180)/(14)\\\\\\Mean=(580)/(14)\\\\\\Mean=41.42857`

• 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:

`Mean=(10* 2+20* 4+30* 4+40+50* 2+60)/(14)\\\\\\Mean=(420)/(14)\\\\\\Mean=30`

• 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 )