Quantitative Statistical Assignment

Question 1
The following data are IQ scores for 50 persons. (p. 44)
141 115 87 91 96 92 118 98 101 107
97 118 124 146 108 106 135 97 108 129
107 101 110 129 109 83 127 116 113 105
127 112 114 114 139 109 102 113 106 89
108 102 92 102 134 104 101 131 86 123
Construct a grouped frequency distribution, using an interval width (w) of 10. Note each interval of the group frequency distribution should begin with a multiple of the interval width. This means that you won’t begin with the lowest of the 50 scores given above.
Solution
N=50
W=10
Max Value-Min Value= 146-83=63
Number of classes=63/10=6.3. Approximately 7 classes
Class Limits Class Boundaries Frequency (f) Cumulative frequency
80-89 79.5-89.5 4 4
90-99 89.5-99.5 7 11
100-109 99.5-109.5 17 28
110-119 109.5-119.5 10 38
120-129 119.5-129.5 6 44
130-139 129.5-139.5 4 48
140-149 139.5-149.5 2 50

Question 2.
Which of these correlation coefficients indicates the strongest relationship?
a. .55
b. .09
c. -.77
d. .10
Solution
Correlation coefficients make it possible to evaluate the strength of association existing between two variables. The values of correlation coefficients usually range from -1 to 1. The strongest linear relationship is normally the one close to -1 or 1. In this case, it is quite apparent that the right answer is (c)-0.77.
Question 3
In a dataset, the X-observations below tend to be associated with Y-observations above, which of correlation coefficients in Question 2 best reflects this relationship between X and Y? (Note = mean of all X scores and = mean of all Y scores)
Solution
This scenario is normally referred to as the maximum positive correlation, where r=1.

0.The correlation coefficient in Question 2 that best reflects the maximum positive correlation is (a) .55.
Question 4
Select the scatter diagram that best matches the relationship described
Solution
(2) About +.50Moderate direct relationship
3696970-175895
Question 5
Questions a to g refer to the following distribution of observations of X: 1, 3, 6, 8, 9, 9, 10, 10, 10
What is the value of the mode? 10
What is the value of n? 9
What is the value of the median? 9
What is the value of ΣX? 66 What is the value of the mean? 7.3333
Describe the shape of the distribution. Binomial distributionWhat is the value of the range? (max. value-min. value)/n; (10-1)/9=1
What is the value of the standard deviation
X (X-MEAN)2
1 40.11
3 18.78
6 1.78
8 1.78
9 5.44
9 5.44
10 7.11
10 7.11
10 7.11
∑(x-mean) 2 = 92.99
Standard deviation = ∑(x-mean) 2
n
=92.99/9= 10.3322
Question 6
Information on certain standardized intelligence and achievement tests is given below. Answer questions 6 to 16 assuming scores are normally distributed.
Iowa Test of Basic Skills Grade-Equivalent Scores
Reading Arithmetic
Wechsler IQ Grade 3 Grade 5 Grade 8 Grade 5
100 3.0 5.0 8.0 5.0
μ σ 15 1.0 1.4 1.9 1.1
An IQ score above 115 is obtained by what percent of the population?
Since the intelligence scores from a normal curve, roughly 34 % of the scores are between the mean (100) and the standard deviation (15) above the mean. For a normal distribution, 50 % of the scores fall below the meanwhile 50 % fall above the mean. Therefore, about 84 %( 50 % below mean and 34 %between mean and the score of 115) of scores are below 115. As such, since 84 % fall under 115, therefore16 % (100 % – 84 %) must fall above the 115 score of 115.
If a fifth-grade student obtains a percentile rank of 84 in reading, what is the grade-equivalent score? 115
What is the grade-equivalent score for the same relative performance as in question 2 (P84) in arithmetic at grade 5? 4.2
Jack was reading at 6.1 when he entered grade 8. If his Wechsler IQ is equivalent to the same percentile rank, what is it? At 76th percentile, therefore (76*115)/84= 104
If Jack’s score in question 9 is valid, he reads better than about what percentage of children in his grade? 74%
Upon entering grade 3, approximately what percent of third-grade children:
a. Obtains a reading grade-equivalent score of 3.0 or better? 37%
b. Obtains a score of 4.0 or better? 16%
c. Obtains a score of 5.0 or better? 5%
12. On the reading test, what percent of beginning third-grade students (3.0) score no higher than the average beginning second-grade students (2.0)? 63%
13. At grade 5, is a grade-equivalent score of 6.0 relative better (i.e., does it have a higher percentile equivalent) in arithmetic than in reading? It is relatively better since it has a higher percentile equivalent in arithmetic than in reading.
In reading, what percentage of third-grade students score below grade-equivalent scores of 2.0, 3.0, 4.0, and 5.0, respectively? 33%, 50%, 67%, and 83.3%.
How much reading gain in grade-equivalent units is required during the five years between grade 3.0 and 8.0 to:
d. Maintain a percentile equivalent of 50? 8.0
e. Maintain a percentile equivalent of 84? 13.44
16. If X3 = 176 with μ = 163 and σ = 26, express X3 as a z-score.
z = (X3 – μ) / σ
= (176-163)/ 26
=0.5
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