A website publishes data on U.S colleges and universities. For the seven primarily undergraduate public universities in California with enrollments between 10,000 and 20,000, six year graduation rates and student-related expenditures (in thousands) per fulltime student for 2007 were reported as shown in Table 1. Table 1 oberservation graduation rate student-related expenditure(in thousand $) 1 66.1 8.80 2 52.4 7.70 3 48.9 8.10 4 48.1 8.40 5 42.0 8.50 6 38.3 7.35 7 31.3 7.95 (i) Given the graduation rate and the student-related expenditure, complete the table below. x y xy y2 x2 8.80 66.1 7.70 52.4 8.10 48.9 8.40 48.1 8.50 42.0 7.35 38.3 7.95 31.3 (ii) Using Pearson’s Correlation Coefficient formula, find the correlation r value of the data above.
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.
A website publishes data on U.S colleges and universities. For the seven primarily undergraduate
public universities in California with enrollments between 10,000 and 20,000, six year graduation
rates and student-related expenditures (in thousands) per fulltime student for 2007 were
reported as shown in Table 1.
Table 1
| oberservation | graduation rate | student-related expenditure(in thousand $) |
| 1 | 66.1 | 8.80 |
| 2 | 52.4 | 7.70 |
| 3 | 48.9 | 8.10 |
| 4 | 48.1 | 8.40 |
| 5 | 42.0 | 8.50 |
| 6 | 38.3 | 7.35 |
| 7 | 31.3 | 7.95 |
(i) Given the graduation rate and the student-related expenditure, complete the table below.
| x | y | xy | y2 | x2 |
| 8.80 | 66.1 | |||
| 7.70 | 52.4 | |||
| 8.10 | 48.9 | |||
| 8.40 | 48.1 | |||
| 8.50 | 42.0 | |||
| 7.35 | 38.3 | |||
| 7.95 | 31.3 |
(ii) Using Pearson’s
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