Econ 310, Spring 2014- Week 2:
Question 1: Calculate the mean, median, mode, and variance of the following students grades:
Table: Data Categories
|
Student
|
Grade
|
Tom
|
80
|
Sean
|
90
|
Ed
|
60
|
Ben
|
70
|
Nate
|
80
|
How do you interpret the standard deviation? Here's a "Rule of Thumb", dubbed the "Empirical Rule": If the histogram of the data is approximately bell-shaped, then:
i. Approximately 68% of all observations fall within 1 standard devation of the mean.
ii. Approximately 95% of all observations fall within 2 standard devation of the mean.
iii. Approximately 99.7% of all observations fall within 3 standard devation of the mean.
But, more generally, Chebysheff's Theorem says: the fraction of observations in any sample or population that lie within k standard deviations of the mean is at least:
1 - 1/k2 for k > 1
Another way of measuring variation is through percentiles. For example, the 25th percentile of data (first quartile) is where 25% of the data is below a value and 75% of the data is above. The interquartile range is the difference between the third quartile and the first quartile.
Question 2: Calculate the variance of the following grade data. How much data falls within 1 standard deviation of the data? Does it correspond with the empirical rule? Does it correspond with Chebysheff's Theorem? What is the interquartile range?
Table 3: Data Categories
|
Student
|
Grade
|
Did you eat ice cream before the exam?
|
1
|
1
|
0
|
2
|
2
|
0
|
3
|
2
|
1
|
4
|
3
|
1
|
5
|
3
|
1
|
6
|
3
|
0
|
7
|
4
|
0
|
8
|
4
|
1
|
9
|
5
|
1
|
10
|
6
|
0
|
Question 3: Correlations. From the above data, calculate the covariance and correlation between grade and ice cream consumption. Can you infer anything? What does the correlation number mean?
Question 4: Interpret this figure plot
![787_Figure.png](https://secure.tutorsglobe.com/CMSImages/787_Figure.png)