Quiz Results EQR Study Hrs Age Sex BBT MB MC AuHS LM 15 10 3 19 0 0 1 1 0 1 14 15 4 24 0 0 1 0 0 1 9 15 1 20 0 10 1 0 0 1 6 10 3 21 0 0 1 1 0 1 14 15 4 21 0 9 1 0 0 1 12 10 6 21 0 2 0 1 0 1 12 13 2 21 1 8 1 0 0 0 15 15 0 20 0 8 1 0 0 1 12 15 3 20 0 10 1 0 0 1 13 15 0.2 19 0 8 1 0 0 1 15 15 2 20 0 6 1 0 1 1 12 14 5 20 0 5 1 1 1 1 14 15 7 22 0 8 0 0 0 0 7 7 10 21 1 7 0 0 1 0 11 15 5 24 0 0 1 0 0 1 10 10 3 22 1 0 1 0 0 1 13 11 3 23 1 1 1 1 1 1 13 15 2 22 1 8 0 0 0 0 13 12 4 20 1 7 1 0 1 0 13 10 3 20 1 0 1 0 0 1 8 13 5 20 1 8 0 0 0 0 12 13 5 22 0 5 0 0 0 1 13 15 8 22 0 5 0 1 0 1 10 13 4 23 1 7 1 0 0 1 13 13 0.5 20 1 0 0 0 0 0 12 13 0.5 20 1 0 1 0 0 0 15 15 2 21 0 10 1 0 0 1 10 13 6 22 0 6 1 1 0 1 11 8 5 20 0 10 0 0 1 0 12 10 4 19 1 0 1 0 0 1 8 5 2 20 1 0 1 0 1 0 11 13 6 20 1 7.5 1 1 1 1 10 3 12 21 0 4 1 0 1 0 8 11 2 19 0 0 1 0 0 1 15 15 3 23 1 2 1 0 0 1 11 14 1 23 0 10 1 1 1 1 13 14 4 21 1 8 1 0 1 1 9 15 3 22 0 5 1 0 0 0 13 14 4 21 0 9 1 0 0 1 13 15 4 20 0 5 1 0 0 1 11 13 5 20 1 8 0 0 0 0 7 10 3 24 1 5 1 0 1 1 14 15 3 20 0 6 1 0 0 1 13 15 3 20 0 8 0 0 0 0 8 12 0.5 22 1 2 1 1 0 1 8 10 4 19 1 7 0 0 1 1 15 15 3 20 0 7 1 0 0 1 14 14 3 19 0 8 1 0 0 1 7 10 3 21 1 0 0 0 1 0 11 13 2 21 0 7 1 1 0 1 14 15 6 22 0 6 1 0 0 1 9 12 3 21 1 0 1 0 0 1 14 15 2 22 0 5 1 0 0 1 9 8 4 21 0 7 1 0 1 1 15 15 7 20 0 6 1 0 0 1 13 14 3 23 1 4 0 1 0 0 14 15 5 21 0 5 1 0 0 1 12 13 5 19 1 6 1 0 0 0 14 12 2 22 1 10 1 0 0 1 14 13 2 22 0 10 1 0 0 0 11 12 3 22 0 8 1 0 1 1 4 1 9 30 0 10 1 0 1 1 14 15 3 21 1 8 1 0 0 1 15 15 3 20 0 0 0 0 0 0 13 15 3 19 1 7 1 0 0 1 14 15 2 21 1 6 1 0 0 1 8 5 3 20 0 0 1 0 1 1 7 10 9 21 1 0 1 1 0 1 12 14 4 20 0 0 1 0 0 0 6 8 4 21 0 1 1 1 0 0 9 10 5 20 0 2 0 0 1 0 10 13 2 20 1 6 1 1 1 0 10 12 1 25 1 5 1 0 1 1 13 15 2 21 1 3 1 0 0 1 9 8 1 29 0 0 0 1 0 0 12 13 2 19 0 0 1 0 0 1 12 15 3 20 0 0 1 0 0 1 14 12 7 19 0 3 1 0 1 1 8 7 1 19 1 0 0 1 0 0 14 12 1 23 1 6 1 0 1 1 11 9 3 20 1 5 0 1 1 1 13 15 2 21 1 0 1 0 0 1 14 11 2 19 1 9 0 0 0 0 11 14 4 22 1 10 0 0 0 1 10 8 5 20 1 5 0 0 1 1 11 13 1 22 1 2 0 0 0 0 14 15 0.5 20 0 8 1 0 0 0 12 14 15 23 0 0 1 1 0 1 10 12 4 19 1 0 0 1 1 1 14 12 0 20 1 3 1 0 1 1 13 10 2 19 1 0 1 0 1 0 15 12 2 20 1 3 1 0 1 1 8 10 3 19 1 1 1 0 1 1 14 12 5 21 0 0 1 0 0 1 6 10 2 21 1 8 1 0 0 1 8 8 2 21 1 1 1 0 1 1 12 10 2 20 0 7 1 0 1 1 9 6 3 20 0 1 1 1 1 1 7 8 4 19 1 9 1 1 1 0 13 11 6 19 1 6 1 0 0 1 13 10 2 25 1 0 1 0 0 1 14 14 2 25 1 5 1 0 0 0 Create a histogram showing the distribution of marks and study hours. Find the 5-number summary of the distribution of marks and study hours. Comment on the shape of the distribution: is it symmetrical? If it is not, is it positively or negatively skewed? Are there any outliers present? If so, are they of particular interest?
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.
Quiz Results | EQR | Study Hrs | Age | Sex | BBT | MB | MC | AuHS | LM |
15 | 10 | 3 | 19 | 0 | 0 | 1 | 1 | 0 | 1 |
14 | 15 | 4 | 24 | 0 | 0 | 1 | 0 | 0 | 1 |
9 | 15 | 1 | 20 | 0 | 10 | 1 | 0 | 0 | 1 |
6 | 10 | 3 | 21 | 0 | 0 | 1 | 1 | 0 | 1 |
14 | 15 | 4 | 21 | 0 | 9 | 1 | 0 | 0 | 1 |
12 | 10 | 6 | 21 | 0 | 2 | 0 | 1 | 0 | 1 |
12 | 13 | 2 | 21 | 1 | 8 | 1 | 0 | 0 | 0 |
15 | 15 | 0 | 20 | 0 | 8 | 1 | 0 | 0 | 1 |
12 | 15 | 3 | 20 | 0 | 10 | 1 | 0 | 0 | 1 |
13 | 15 | 0.2 | 19 | 0 | 8 | 1 | 0 | 0 | 1 |
15 | 15 | 2 | 20 | 0 | 6 | 1 | 0 | 1 | 1 |
12 | 14 | 5 | 20 | 0 | 5 | 1 | 1 | 1 | 1 |
14 | 15 | 7 | 22 | 0 | 8 | 0 | 0 | 0 | 0 |
7 | 7 | 10 | 21 | 1 | 7 | 0 | 0 | 1 | 0 |
11 | 15 | 5 | 24 | 0 | 0 | 1 | 0 | 0 | 1 |
10 | 10 | 3 | 22 | 1 | 0 | 1 | 0 | 0 | 1 |
13 | 11 | 3 | 23 | 1 | 1 | 1 | 1 | 1 | 1 |
13 | 15 | 2 | 22 | 1 | 8 | 0 | 0 | 0 | 0 |
13 | 12 | 4 | 20 | 1 | 7 | 1 | 0 | 1 | 0 |
13 | 10 | 3 | 20 | 1 | 0 | 1 | 0 | 0 | 1 |
8 | 13 | 5 | 20 | 1 | 8 | 0 | 0 | 0 | 0 |
12 | 13 | 5 | 22 | 0 | 5 | 0 | 0 | 0 | 1 |
13 | 15 | 8 | 22 | 0 | 5 | 0 | 1 | 0 | 1 |
10 | 13 | 4 | 23 | 1 | 7 | 1 | 0 | 0 | 1 |
13 | 13 | 0.5 | 20 | 1 | 0 | 0 | 0 | 0 | 0 |
12 | 13 | 0.5 | 20 | 1 | 0 | 1 | 0 | 0 | 0 |
15 | 15 | 2 | 21 | 0 | 10 | 1 | 0 | 0 | 1 |
10 | 13 | 6 | 22 | 0 | 6 | 1 | 1 | 0 | 1 |
11 | 8 | 5 | 20 | 0 | 10 | 0 | 0 | 1 | 0 |
12 | 10 | 4 | 19 | 1 | 0 | 1 | 0 | 0 | 1 |
8 | 5 | 2 | 20 | 1 | 0 | 1 | 0 | 1 | 0 |
11 | 13 | 6 | 20 | 1 | 7.5 | 1 | 1 | 1 | 1 |
10 | 3 | 12 | 21 | 0 | 4 | 1 | 0 | 1 | 0 |
8 | 11 | 2 | 19 | 0 | 0 | 1 | 0 | 0 | 1 |
15 | 15 | 3 | 23 | 1 | 2 | 1 | 0 | 0 | 1 |
11 | 14 | 1 | 23 | 0 | 10 | 1 | 1 | 1 | 1 |
13 | 14 | 4 | 21 | 1 | 8 | 1 | 0 | 1 | 1 |
9 | 15 | 3 | 22 | 0 | 5 | 1 | 0 | 0 | 0 |
13 | 14 | 4 | 21 | 0 | 9 | 1 | 0 | 0 | 1 |
13 | 15 | 4 | 20 | 0 | 5 | 1 | 0 | 0 | 1 |
11 | 13 | 5 | 20 | 1 | 8 | 0 | 0 | 0 | 0 |
7 | 10 | 3 | 24 | 1 | 5 | 1 | 0 | 1 | 1 |
14 | 15 | 3 | 20 | 0 | 6 | 1 | 0 | 0 | 1 |
13 | 15 | 3 | 20 | 0 | 8 | 0 | 0 | 0 | 0 |
8 | 12 | 0.5 | 22 | 1 | 2 | 1 | 1 | 0 | 1 |
8 | 10 | 4 | 19 | 1 | 7 | 0 | 0 | 1 | 1 |
15 | 15 | 3 | 20 | 0 | 7 | 1 | 0 | 0 | 1 |
14 | 14 | 3 | 19 | 0 | 8 | 1 | 0 | 0 | 1 |
7 | 10 | 3 | 21 | 1 | 0 | 0 | 0 | 1 | 0 |
11 | 13 | 2 | 21 | 0 | 7 | 1 | 1 | 0 | 1 |
14 | 15 | 6 | 22 | 0 | 6 | 1 | 0 | 0 | 1 |
9 | 12 | 3 | 21 | 1 | 0 | 1 | 0 | 0 | 1 |
14 | 15 | 2 | 22 | 0 | 5 | 1 | 0 | 0 | 1 |
9 | 8 | 4 | 21 | 0 | 7 | 1 | 0 | 1 | 1 |
15 | 15 | 7 | 20 | 0 | 6 | 1 | 0 | 0 | 1 |
13 | 14 | 3 | 23 | 1 | 4 | 0 | 1 | 0 | 0 |
14 | 15 | 5 | 21 | 0 | 5 | 1 | 0 | 0 | 1 |
12 | 13 | 5 | 19 | 1 | 6 | 1 | 0 | 0 | 0 |
14 | 12 | 2 | 22 | 1 | 10 | 1 | 0 | 0 | 1 |
14 | 13 | 2 | 22 | 0 | 10 | 1 | 0 | 0 | 0 |
11 | 12 | 3 | 22 | 0 | 8 | 1 | 0 | 1 | 1 |
4 | 1 | 9 | 30 | 0 | 10 | 1 | 0 | 1 | 1 |
14 | 15 | 3 | 21 | 1 | 8 | 1 | 0 | 0 | 1 |
15 | 15 | 3 | 20 | 0 | 0 | 0 | 0 | 0 | 0 |
13 | 15 | 3 | 19 | 1 | 7 | 1 | 0 | 0 | 1 |
14 | 15 | 2 | 21 | 1 | 6 | 1 | 0 | 0 | 1 |
8 | 5 | 3 | 20 | 0 | 0 | 1 | 0 | 1 | 1 |
7 | 10 | 9 | 21 | 1 | 0 | 1 | 1 | 0 | 1 |
12 | 14 | 4 | 20 | 0 | 0 | 1 | 0 | 0 | 0 |
6 | 8 | 4 | 21 | 0 | 1 | 1 | 1 | 0 | 0 |
9 | 10 | 5 | 20 | 0 | 2 | 0 | 0 | 1 | 0 |
10 | 13 | 2 | 20 | 1 | 6 | 1 | 1 | 1 | 0 |
10 | 12 | 1 | 25 | 1 | 5 | 1 | 0 | 1 | 1 |
13 | 15 | 2 | 21 | 1 | 3 | 1 | 0 | 0 | 1 |
9 | 8 | 1 | 29 | 0 | 0 | 0 | 1 | 0 | 0 |
12 | 13 | 2 | 19 | 0 | 0 | 1 | 0 | 0 | 1 |
12 | 15 | 3 | 20 | 0 | 0 | 1 | 0 | 0 | 1 |
14 | 12 | 7 | 19 | 0 | 3 | 1 | 0 | 1 | 1 |
8 | 7 | 1 | 19 | 1 | 0 | 0 | 1 | 0 | 0 |
14 | 12 | 1 | 23 | 1 | 6 | 1 | 0 | 1 | 1 |
11 | 9 | 3 | 20 | 1 | 5 | 0 | 1 | 1 | 1 |
13 | 15 | 2 | 21 | 1 | 0 | 1 | 0 | 0 | 1 |
14 | 11 | 2 | 19 | 1 | 9 | 0 | 0 | 0 | 0 |
11 | 14 | 4 | 22 | 1 | 10 | 0 | 0 | 0 | 1 |
10 | 8 | 5 | 20 | 1 | 5 | 0 | 0 | 1 | 1 |
11 | 13 | 1 | 22 | 1 | 2 | 0 | 0 | 0 | 0 |
14 | 15 | 0.5 | 20 | 0 | 8 | 1 | 0 | 0 | 0 |
12 | 14 | 15 | 23 | 0 | 0 | 1 | 1 | 0 | 1 |
10 | 12 | 4 | 19 | 1 | 0 | 0 | 1 | 1 | 1 |
14 | 12 | 0 | 20 | 1 | 3 | 1 | 0 | 1 | 1 |
13 | 10 | 2 | 19 | 1 | 0 | 1 | 0 | 1 | 0 |
15 | 12 | 2 | 20 | 1 | 3 | 1 | 0 | 1 | 1 |
8 | 10 | 3 | 19 | 1 | 1 | 1 | 0 | 1 | 1 |
14 | 12 | 5 | 21 | 0 | 0 | 1 | 0 | 0 | 1 |
6 | 10 | 2 | 21 | 1 | 8 | 1 | 0 | 0 | 1 |
8 | 8 | 2 | 21 | 1 | 1 | 1 | 0 | 1 | 1 |
12 | 10 | 2 | 20 | 0 | 7 | 1 | 0 | 1 | 1 |
9 | 6 | 3 | 20 | 0 | 1 | 1 | 1 | 1 | 1 |
7 | 8 | 4 | 19 | 1 | 9 | 1 | 1 | 1 | 0 |
13 | 11 | 6 | 19 | 1 | 6 | 1 | 0 | 0 | 1 |
13 | 10 | 2 | 25 | 1 | 0 | 1 | 0 | 0 | 1 |
14 | 14 | 2 | 25 | 1 | 5 | 1 | 0 | 0 | 0 |
Create a histogram showing the distribution of marks and study hours. Find the 5-number summary of the distribution of marks and study hours. Comment on the shape of the distribution: is it symmetrical? If it is not, is it positively or negatively skewed? Are there any outliers present? If so, are they of particular interest?
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