# The Variance of a Random Variable Is Sensitive to Outliers

**Introduction to Statistics**

Supplemental Instruction

Iowa State University / Leader: / Ben

Course: / STAT 226

Instructor: / Dr. Genschel

Date: / 21 September

True/False Practice

The variance of a random variable is sensitive to outliers.

The median of a random variable is sensitive to a single outlier

The 40th percentile of a probability function is the value x such that P(X>x) = .4

If the mean of a normally distributed function is shifted to the left by 100, the mean will decrease and the variance will increase.

Histograms intervals cannot be re-arranged in any order the user desires, but the user can manipulate the length of the intervals on a histogram.

- A vacuum manufacturing company creates vacuums. After careful research, it is assumed that the manufacturing process follows this distribution X~N(35, 32) for vacuum heights.

What is the population in this example?

What is the parameter of interest?

Describe a potential sample of this population.

What percentage of vacuums are between 31 and 38 inches high?

A random sample of vacuums was taken over the course of a day. 10 vacuums height was measured for quality control purposes. What is the mean and standard error for this sample?

What is the probability that one of the sample vacuums was between 31 and 38 inches high in the sample distribution?

Explain the difference in the probabilities between the population and sample population size. What happens to the standard error when the sample size is increased by 5? When decreased by 5?

- A company wants to know the average height of students that attend Iowa State. Assume that the population is normally distributed with the following distribution, X~N(130,102)

What is the population in this example?

Describe a potential sample for this population.

What is the parameter of interest?

What would be an example of a statistic for a hypothetical sample?

What height would correspond with the 20th percentile?

The University decides to perform an analysis and surveys 25 students. What would be the mean and standard error for the sample?

What is the probability that a student is taller than 135 units in the sample distribution?

- A swimming test is scored using a rubric. The population has a mean of 200 and standard deviation of 15. The distribution is not normally distributed.

Describe the way that a researcher could analyze the results and make a sample follow a normal distribution.

Assume that a sample of 30 people is taken and this meets the requirements of the Cental Limit Theorm.

What proportion of people score between 195 and 205 on the swimming test?