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. 3; 7; −1; 1; 0; 5; −3; 2; −1; 6; 5; −2

1. μ = 1.83 (rounding to the next hundredth)

2. σ = 3.21 (rounding to the next hundredth)

3. Median = 3/3 = 1.5

4. Score = - 5.232

Correct statement and question:

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a 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 12 change scores are as follows:

3; 7; −1; 1; 0; 5; −3; 2; −1; 6; 5; −2

1. What is the mean change score?

2. What is the standard deviation for this sample?

3. What is the median change score?

4. Find the change score that is 2.2 standard deviations below the mean.

Source: Previous question that can be found at

Step-by-step explanation:

1. Let's calculate the mean change score, this way:

μ = (3 + 7 + -1 + 2 + 0 + 5 + -3 + 1 + -1 + 6 + 5 + -2)/12

μ = 22/12

μ = 1.83 (rounding to the next hundredth)

2. Let's calculate the standard deviation, this way:

σ² = [(3² - 1.83²) + (7² - 1.83²) + (-1² - 1.83²) +( 1² -1.83²) + (0² - 1.83²) + (5 - 1.83²) + (-3² - 1.83²) + (2² - 1.83²) + ( -1² - 1.83²) + (6² - 1.83²) + (5² - 1.83²) + (-2² - 1.83²=]/12

σ² = 123.67/12

σ² = 10.31

√σ² = √10.31

σ = 3.21 (rounding to the next hundredth)

3. Let's calculate the median change score, this way:

Let's recall that If you have an even set of numbers, average the middle two to find the median, therefore we have:

-3/-2/-1/-1/0/1/2/3/5/5/6/7

Median = (1 + 2)/2

Median = 3/3 = 1.5

4. Let's find the change score that is 2.2 standard deviations below the mean, this way:

Score = 1.83 - 2.2 * 3.21

Score = 1.83 - 7.062

Score = - 5.232

4.08%

step-by-step explanation: