Use the following dataset of a small population (N=9). (4 marks) 71, 74, 76, 77, 78, 84, 86, 90, 93 Calculate and report: the mean the Sum of Squares the Variance the Standard Deviation How would each...

1. the mean


2. the Sum of Squares


3. the Variance


4. the Standard Deviation

1. you were given exactly the same dataset, but it was for a sample?(2 marks)
   


2. each of the values was multiplied by 5?(2 marks)
   

1. the mean


2. the Sum of Squares


3. the Standard Deviation


4. Compare the mean and standard deviation calculated for question 19 versus question 21. What was the effect of a single extreme value?

Calculate each Z score and interpret it using the following criteria:(5 marks)

Between -1 and +1 = Average
From -1 to -2 = Below Average
From +1 to +2 = Above Average
Below -2 = Extremely Low
Above +2 = Extremely High

1. 
   

   X = 48 µ= 62 σ= 10

   
   


2. 
   

   X = 110 µ= 130 σ= 24

   
   


3. 
   

   X = 110 µ= 65 σ= 20

   
   


4. 
   

   X = 104 µ= 75 σ= 18

   
   


5. 
   

   X = 17.4 µ= 15.9 σ= 2.4

   
   

Lee scored exactly 80 on two different tests, but received very different letter grades. Use your knowledge of central tendency, variability, and standard scores to clarify the reason for the difference in grades. In professional life, Z scores are often converted to T scores (which use a mean of 50 and a standard deviation of 10). This avoids dealing with negative values.(6 marks)

You need the mean and standard deviation for each test.
Sociology: µ = 86 σ = 4
Biology: µ = 74 σ = 8

1. 
   

   Convert Lee’s scores to Z scores and T scores

   
   


2. 
   

   Use central tendency, variability, and the interpretation criteria from question 22 to explain the difference in grades.

   
   

1. Sherlock’s score was 800.
   What is his Z score?
   What proportion of the population would be expected to score higher?


2. Watson’s score was 475.
   What is his Z score?
   What percent of the population would be expected to score lower?

1. What Z score must be achieved?


2. What T score must be achieved?


3. What raw score must be achieved?