Below are the scores of 35 grade 11 students in the final examinations in Mathematics. 61 76 68 82 90 68 93 45 54 54 79 83 58 75 70 63 72 72 77 50 100 72 98 90 96 83 89 86 85 95 88 91 68 65 57 What value corresponds to the 40th percentile ? 2. What is the percentile rank of the score 85? 3. What value corresponds to Q3 ? 4. If the passing grade is 75, how many percent of the students will fail? 5. If a grade of at least 90 is required to be included in the honor role, how many percent of the students are qualified? Answer
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Below are the scores of 35 grade 11 students in the final examinations in Mathematics.
|
61 |
76 |
68 |
82 |
90 |
68 |
93 |
|
45
|
54 |
54 |
79 |
83 |
58 |
75 |
|
70 |
63 |
72 |
72 |
77 |
50 |
100 |
|
72 |
98 |
90 |
96 |
83 |
89 |
86 |
|
85 |
95 |
88 |
91 |
68 |
65 |
57 |
- What value corresponds to the 40th percentile ?
2. What is the percentile rank of the score 85?
3. What value corresponds to Q3 ?
4. If the passing grade is 75, how many percent of the students will fail?
5. If a grade of at least 90 is required to be included in the honor role, how many percent of the students are qualified?
Answer:
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