Question

A school district is deciding whether or not to adopt a new social skills curriculum. Three classrooms are randomly selected as test sites for the curriculum. To obtain a measure of student improvement, students in the three classrooms are tested on their social skills before and after the curriculum is implemented. The social skills test has 25 possible points. The post-implementation scores for the students in the first classroom are shown in the following table: 22 21 16 18 15 23 17 24 20 19 22 11
Calculate the sample size, n; the total sum, ΣX; and the sample mean, M.
n =
ΣX =
M =
The school district decides it will be easier to understand the scores if they are converted to a 10-point scale. This requires that each score be divided by 2.50.
Calculate the new n, ΣX, and M.
n =
ΣX =
M =

Answer 1

Answer and Explanation:

The computation is shown below:

Given that

sample size n = 12

$\sum X$ = 22 + 21 + 16 + 18 + 15 + 23 + 17 + 24 + 20 + 19 + 22 + 11

= 228

Now

sample mean M is

$= \sum X \div n$

= 228 ÷ 12

= 19

In the case when the each score would be divided by 2.5 so the size of the sample would remains the same But $\sum X$ and M would be

$\sum X \div 2.5 \\\\M \div 2.5$

Now

New n = 12

$New \sum X = Old \sum X \div 2.5$

= 228 ÷ 2.5

= 91.2

New Mean = Old mean ÷ 2.5  

= 19 ÷ 2.5

= 7.6