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.

3; 9; −1; 2; 0; 4; −3; 1; −1; 5; 4; −2

• Part (b)

  What is the standard deviation for this sample? (Round your answer to two decimal places.)

• Part (c)

  What is the median change score? (Round your answer to one decimal place.)

• Part (d)

  Find the change score that is 2.2 standard deviations below the mean. (Round your answer to one decimal place.)

Answer 1

Answer

first, we need to arrange the data in ascending order

-3, -2, -1, -1, 0, 1, 2, 3, 4, 4, 5, 9

(B) We need to find the mean value in order to calculate the standard deviation

Mean = (sum of all values)/(total number of values) = (-3 - 2 - 1 - 1 + 0 + 1 + 2 + 3 + 4 + 4 + 5 + 9)/12 = 21/12= 1.75

Now, we know the formula for standard deviation

where xi are given 12 values and x(bar) is mean = 1.75 and n is the sample size = 12

So, sample standard deviation is s = 3.44 (rounded to two decimals)

(c) We have 12 data values, i.e. even number of data values.

Formula for median for even data values is given as

Medain = ((n/2)th term + (n/2)+1 term)/2

where n is 12

so, we get

Medain = ((12/2)th term + (12/2)+1 term)/2 = (6th term + 7th term)/2 = (1+2)/2 = 3/2 = 1.5

So, median is 1.5

(d) 2.2 standard deviation below the mean can be written as mean-(2.2*s)

where mean = 1.75 and s = 3.44

setting the values in the above equation, we get

1.75 - (2.2*3.44) = 1.75 - 7.568 = -5.8

So, required value is -5.8