Assignment

1. A population consists of five observations: A = {10, 6, 8, 9, 12}

a) Calculate the mean of the data set.
b) Calculate the standard deviation of the data set.
c) What are the new values of the mean and the standard deviation if the same constant k is added to each data value in the given set?
d) What are the new values of the mean and the standard deviation if each data value of the set is multiplied by the same constant k?

2. A national achievement test has a mean score of 150 and a standard deviation of 25. The z-score for student A is 1.2, for student B is 0.9.

Who gets higher score and what is the score?

3. For the following set of data {(-1, 0), (0, 2), (1, 4), (2, 5)}
a) Find the slope and intercept of the least square regression line
b) Compute the R-squared (The coefficient of determination) by:
R-squared = SSR / SST = 1 ? SSE / SST
c) Estimate the value of y for x = 1.9

Answer:

1) Given data set
{10, 6,8,9, 12}
A) Mean = (sum of the observations}/{number of observations}
Mean = {10+6+8+9+12}/5 = 9
B) To find the standard deviation first we need to subtract mean from each and every observation and then we need to take the square and finally we need to add them
(10-9)^2 + (6-9)^2 +...
= 20
Now we need to divide this by number of observations and take the square root
Standard deviation = ?{20/5} = 2
C) If the same value would he added to each value for example 2
Then new data would be
{12, 8, 10, 11, 14}
Mean = {12 + 8 + 10 + 11 + 14}/5 = 11
That is mean is also increased by 2
For standard deviation
It would be same
As the standard deviation is the average distance between values and mean
So as each and every number is added with same constant
S.d would be same
So the conclusion is that
If same constant k is added to each and every data value then, mean would be increased by the same value
And s.d would be unaffected
Mean = 9+k
S.d = 2 only