Question

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows. 4; 7; −1; 1; 0; 5; −3; 2; −1; 6; 5; −2(a) What is the mean change score?
(b) What is the standard deviation for this population?
(c) What is the median change score?
(d) Find the change score that is 2.2 standard deviations below the mean.

Answer 1

Answer:

a) 1.9

b) 3.25

c) 1.5

d) -5.25

Step-by-step explanation:

We are given the following in the data:

4, 7, -1, 1, 0, 5, -3, 2, -1, 6, 5, -2

a) Mean change score

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{23}{12} = 1.9$

b)  standard deviation for this population

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of differences = 126.92

$S.D = \sqrt{\dfrac{126.92}{12}} = 3.25$

c) median change score

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

$\text{Median} = \dfrac{6^{th}+7^{th}}{2} = \dfrac{1+2}{2} = 1.5$

d) change score that is 2.2 standard deviations below the mean.

$\mu - 2.2(\sigma)\\1.92 - 2.2(3.25) = -5.25$