Question

Ms. Barnsley separates her class into two groups. She gives each student the same 25-question math quiz. Group A uses a calculator, while Group B does not. The table shows the completion times, in minutes, of students in each group.

Which statement is true about the distributions of completion times?

The students in Group A tended to complete the quiz in less time.
The median of Group A is greater than the median of Group B.
The means of both groups are about the same.
The standard deviation of Group B is less than the standard deviation of Group A.

Answer 1

b

Explanation:

Answer 2

The median of Group A is greater than the median of Group B.

Explanation:

Given

Required

Which of the options is true

(a) Group A complete in less time

To do this, we calculate the average of both using:

`\bar x = (\sum x)/(n)`

Where

`n = 9`

So, we have:

`\bar x_A = (4.5 + 4.8 + 4.6 + 5.0 + 4.8 + 4.4 + 4.7 + 5.2 + 3.9)/(9)`

`\bar x_A = (41.9)/(9)`

`\bar x_A = 4.66`

`\bar x_B =(5.5 + 4.9 + 4.0 + 4.2 + 4.8 + 4.1 + 3.5 + 4.6 + 4.3)/(9)`

`\bar x_B =(39.9)/(9)`

`\bar x_B =4.43`

The average time of Group A is higher than that of B, this means that Group A spend more time, on average.

(b) Group A has a greater median

First, we sort the given data in ascending order

The median is then calculated using:

`Median = (n + 1)/(2)th`

This gives:

`Median = (9 + 1)/(2)th`

`Median = (10)/(2)th`

`Median = 5th`

The median is the fifth item for both groups.

So, we have:

`A =4.7`

`B =4.3`

4.7 is greater than 4.3

Hence, (b) is true

Since (b) is true and only one option is correct, then (c) and (d) are incorrect