Statistics: basic descriptive statistics, mean , variance, summation

Statistics Problem Set Aug-21-2012

1. Which of the following formulas measure symmetry of a sample data distribution?

(a)$(1/n) \sum (x-\overline{x})^2$

(b) $ (1/n) \sum (x-\overline{x})^3$

(c)$ (1/n) \sum (x-\overline{x})^4$

(d.) Not listed

2. The following were determined for a sample data: n = 10, min=-2, max= 10, sd = 3,
$\overline{x}=5$. The data is invalid since

$max > \overline{x} + (n-1) sd.$

(b) $min < \overline{x} - (n-1) sd$

(c) median is not specified

(d) None of the above.

3. A sample has current mean mean 4.0 with sample size 10. If 5 is added to all sample values, the recomputed mean will :

stay the same!

(b) will increase by 5.0

(c) will decrease by 5

(d)will increase by 0.5 (e) None of the above

4.A sample has current variance of 2.0 with sample size 10. If 5 is added to all sample values, the recomputed variance will :

stay the same!

(b) will increase by 5.0

(c) will decrease by 5

(d)will increase by 0.5

(d) None of the above.

5. The formula $e^{[(1/n)\sum_{i=1}^{i = n} \ln(x_i)}$ is another way of solving for the

(a) HM

(b) GM

(c) AM

(d) RMS.

6. A new data value 2.5 is added to a sample with mean 3 and sample size 10. The recomputed mean will

increase

(b) decrease

(c) stay the same

(d) None of the above

7. A sample has a sample size 10 and median 50, with all sample values unique. If the minimum value in the sample is removed,
the new median will

stay the same!

(b) increase

(c) decrease

(d) None of the above.

8. Express (-1) + 2 + (-3) + 4 + (-5) + 6 in summation form with index k $ of summation varying from 1 to 6. You cannot use
a variable X as these are not stored in an a vector or array!.

9. If X = c( 4,5,6,7,8), what is the value of $\sum_{i=1}^4 (x_i)(x_{i-1})$?.

10.If X is the same above and Y= c(2,3,1,0,4) what is the value of $\sum_{i=1}^5 {(x_i -\overline{x}) (y_i-\overline{y})}$?


Solutions next week! Enjoy first solving.