Statistics 226
Supplemental Instruction
Iowa State University / Leader: / Luyun
Course: / Stat 226
Instructor: / Anna Peterson
Date: / 1/27/16
For questions 1-13, answer true or false. If the statement is false, change it in a way that makes it true. Try to complete this quiz on your own without using your notes.
___1.) The numbers 6, 7, 8, 9have the same standard deviation as 160, 170, 180, 190.
___2.) The quartiles Q1, Q2, and Q3 are numbers that divide an ordered group of observations into 3 equally size groups.
___3.) Q1 is the median of all observations to the left of the median M, including M.
___4.) 75% of all observations in a data set are of lesser value than Q3.
___5.) For a symmetric distribution, Q1 and Q3 are about equally apart from M.
___6.) For a left-skewed distribution, Q1 will be closer to M than Q3.
___7.) For a right-skewed distribution, the minimum is closer to M than the maximum.
___8.) The IQR is equal to the middle 50% of the data.
___9.) The sample variance corresponds to the mean of all deviations of each observation from the sample mean.
___10.) The sample variance, s, is equal to the square root of the standard deviation, s2.
___11.) For the data set 7, 7, 7, 7, 7, 7, 7, 7, the standard deviation is equal to zero, but the variance is equal to 1.
___12.) If a data set is reasonably symmetric and no outliers are present, then we should only use the IQR and 5-number summary as measures of spread and center.
___13.) It is more advantageous to work with standard deviation than variance because standard deviation is expressed in the same units as the observations in the data set.
Group exercise:
- The mean age of 5 persons in a room is 30 years. A 36-year-old person walks in. What is now the mean age of the persons in the room?
- Suppose that the median age is 30 years and a 36-year-old enters. Can you find the new median age from this information?
- For the following set of numbers: 4, 0, 1, 3, 6 the mean, variance and standard deviation are given by x̄=3, s2=4.8, s=2.19
Suppose you add 2 to each of the numbers in the first set. That gives us the set 6, 2, 3, 6, 5, 8.
- Find the mean and the standard deviation of this set of numbers.
- Compare your answer with those for the set given above. How did adding 2 to each number change the mean?
This exercise should help you see that the standard deviation or variance measures only the spread around the mean and ignores changes in where the data are positioned.
- Data was collected on the total play count last.FM users have uploaded to their last.FM accounts. There were over 1 million users in the dataset and multiple variables were collected on this data. We will only consider a sample of 7 of the play counts. The following is the sample of play counts:
310029465339950492792851015199
Some useful things: and =574903907
- Calculate the sample mean.
- Calculate the sample standard deviation.
- Calculate the median and interquartile range.