Question

The dot plots below show the scores for a group of students for two rounds of a quiz: Two dot plots are shown one below the other. The title for the dot plot on the top is Round 1 and the title for the bottom plot is Round 2. Below the line for each dot plot is written Score. There are markings from 1 to 5 on the line at intervals of one. There are 2 dots above the mark 2, there are 3 dots above the mark 3, there are 2 dots above the mark 4 and there is 1 dot above the mark 5. For the bottom dot plot there are there are 4 dots above the mark 4 and there are 4 dots above the mark 5. Which of the following inferences can be made using the dot plots? There is no overlap between the data. Round 2 scores are lower than round 1 scores. Round 1 scores are higher than round 2 scores. The range of round 1 is greater than the round 2 range.

Answer 1

Answer:

The correct option is 4. The range of round 1 is greater than the round 2 range.

Step-by-step explanation:

In the given dot plots the lines represents the scores and the dots above the mark represents its frequency.

For Round 1, the frequency table is:

Score                Frequency

  1                          0

  2                          2

  3                          3

  4                          2  

  5                          1

Total score of round 1 is

$2(2)+3(3)+4(2)+5(1)=26$

From the above table it is clear that the minimum score for round 1 is 2 and the maximum score is 5.

$Range=Maximum-Minimum=5-2=3$

Therefore the range of round 1 is 3.

For Round 2, the frequency table is:

Score                Frequency

  1                          0

  2                         0

  3                         0

  4                          4  

  5                          4

Total score of round 2 is

$4(4)+5(4)=36$

From the above table it is clear that the minimum score for round 2 is 4 and the maximum score is 5.

$Range=Maximum-Minimum=5-4=1$

Therefore the range of round 2 is 1.

There is overlap between the data. Therefore option 1 is incorrect.

Since 36>26, it means the scores of round 2 are higher than round-1, therefore options 2 and 3 are incorrect.

Range of round 1 is 3 and the range of round 2 is 1, therefore the range of round 1 is greater than the round 2 range.

Hence option 4 is correct.

Answer 2

Answer:

The inference that can be made using the dot plot is:

    The range of round 1 is greater than the round 2 range.

Step-by-step explanation:

Round 1:

Score                Frequency

  1                          0

  2                          2

  3                          3

  4                          2  

  5                          1

Hence, the minimum score of Round 1 is: 2

maximum score is: 5

Hence, Range=Maximum value-Minimum score

                      =5-2

                       =3

Similarly, Round-2

Score                Frequency

  1                          0

  2                         0

  3                          0

  4                          4  

  5                          4

Hence, the minimum score of Round 1 is: 4

maximum score is: 5

Hence, Range=Maximum value-Minimum score

                      =5-4

                       =1

The scores of round 2 are higher than round-1.

Since round 2 have a higher frequency for higher scores as compared to round-1.

Hence, Range of round 1 is greater than the range of Round-2.