Workshop 3 Variability Name: _______________________________________ Date Completed: _____________ |

Provide all solutions, answers and requested outputs after each question.

**Question 1.** (a) Can *SS* ever have a value less than
zero? Explain your answer.

(b) What does it mean for a sample to have a standard deviation of zero?

Describe the scores in such a sample.

**Question 2. ** For the sample *X = {2, 4, 1, 3, 2, 1, 2}*,
compute the range and semi-interquartile range

(use the concepts of median and
quartile to compute).

using the computational formula:

Question 4 to 7 is based on the following data:

54 52 51 50 36 55 44 46 57 44 43 52 38 46

55 34 44 39 43 36 55 57 36 46 49 46 49 47

**Question 4. **Construct a stem and leaf display for the data
and describe the distribution.

mean, mode, median, variance, standard deviation

**Question** **6**. Construct a boxplot and determine if a
value of 63 would be an outlier.

**Question 7. **(a)** **Find the 65% of the data and

(b) What percent of the scores are below 47?

**Question 8. **

mean and variance and

(b) if all the scores were divided by 2, how would that affect the mean and variance?

**For the ODS.csv dataset**:

for the pass4th variable.

**Question 10. ** Construct a stem and leaf display and a
boxplot of the data.