Discuss the below:
Q: i) Calculate the mean, median, mode, range, variance, and standard deviation for the IQ scores.
ii) What does the score distribution (shape of frequency distributions) look like for the IQ scores according to symmetry and skewness?
iii) Assuming that the IQ test has a mean of 100 and a standard deviation of 15, how many students fell one standard deviation below the tests mean? Two standard deviations below the tests mean? What percentage of students had an IQ score less than or equal to 70? An IQ score greater or equal to 100? What assumptions could you make about the test scores and suitability of this test for this group of students?
iv) Assuming that the correlation between IQ scores and GPA scores is +0.87, explain what this means.
v) Assuming that the IQ test has national norms and that this sample is from a small, rural school in Texas with a large population of English as a Second Language learners, what types of limitations might you have regarding the suitability and fairness of this test for this sample?
vi) Considering that you are comparing this sample mean to a population (or normative group) mean, would you use a z-test or t-test? Explain your rationale. What are the similarities and differences between the two scores?
Student ID IQ SCORE GPA
1 84 2.5
2 71 2.1
3 62 1.9
4 89 3.1
5 66 1.9
6 109 3.5
7 107 3.2
8 92 3.3
9 67 2
10 112 3.4
11 74 2.5
12 66 2
13 103 2.9
14 114 3.1
15 76 2.2
16 97 2.9
17 70 2.6
18 108 3.9
19 66 1.8
20 88 2.8
21 113 3.8
22 107 3.5
23 82 3
24 110 3.6
25 94 2.9
26 76 2.4
26 82 2.9
28 74 2
29 88 1.7
30 98 3.3