Question

The dot plots show 9 scores on a 10 question trivia game for two students. Select all the statements that must be true.

..
:
2
3
5
6
7
4.
Noah's scores
...
2
3
5
6
7
Jada's scores
Noah's scores have greater variability than Jada's scores.
The standard deviation of Noah's scores is equal to the standard deviation of Jada's scores.
The mean of Noah's scores is greater than the mean of Jada's scores.
Noah scored better than Jada on every assignment.
Using only Noah's scores, the mean is equal to the median
d
e

Answer 1

The correct statements are b, c and e.

Explanation:

Consider the dot plot for Noah and Jada's score in the trivia game.

From the dot plot it is quite clear that the data form a bell-shaped curved or a normal curve.

For the normal distribution:

Mean = Median = Mode

Noah's mean score = 5

Jada's mean score = 3

The standard deviation of a data set is the measure of dispersion of the observations of that data set from their mean.

On closely studying the graphs we can see that the Noah and Jada's scores are almost at a same distance from the mean, i.e. the spread of Noah's score is same as the spread of Jada's score.

So, the correct statements are:

b. The standard deviation of Noah's scores is equal to the standard deviation of Jada's scores.

c. The mean of Noah's scores is greater than the mean of Jada's scores.

e. Using only Noah's scores, the mean is equal to the median