Sis Sigma Statistics

The values in a dataset are: 25. 15. 13. 6. 14. 18, and 11. What is the range of this dataset?

19

The values for samples in a dataset are 32, 18, 9, 13, 8, 14, and 11. What is the range of this dataset?

24

The values in a dataset are 3.5, 2.5, 2.5, 3.5, and 3.0. If Xbar (sample mean) = sigma X / n, what is the mean for the sample?

3

The values in a dataset are 3.5, 2.5, 2.5, 3.5, and 3.0. If median = (n+1) / 2, what is the median of the sample dataset?

3

The values in a dataset are 3.5, 2.5, 2.5, 3.5, and 3.0. What is the mode of the distribution?

3.5 and 2.5

The values in a dataset are 25, 15, 13, 6, 14, 18, and 11. What is the variance for this distribution?

34.95

The values in a dataset are 25, 15, 13, 6, 14, 18, and 11. What is the standard deviation?

5.91

The values for samples in a dataset are 32, 18, 9, 13, 8, 14, and 11. What is the variance of this distribution?

67.33

The values in a dataset are 7.50, 6.75, 7.25, 7.50, and 6.00. If Xbar (sample mean) = sigma X / n, what is the mean for the sample?

7

The values in a dataset are 7.50, 6.75, 7.25, 7.50, and 6.00. If median = (n+1) / 2, what is the median of the sample dataset?

7.25

The values in a dataset are 7.50, 6.75, 7.25, 7.50, and 6.00. What is the mode of the sample?

7.50

The values for samples in a dataset are 32, 18, 9, 13, 8, 14, and 11. What is the standard deviation of the dataset?

8.21

Match the kinds of statistics with the statements that apply to each of them. Statistic types may match to more than one statement.

Descriptive statistics Use tools such as histograms, measures of central tendency and dispersion, and bar charts Summarize data to make decisions about the present situation Inferential statistics Use techniques such as hypothesis testing, ANOVA, correlation, and regression Use a deductive approach

Match tools for drawing valid statistical conclusions to descriptions of their uses. Some tools may match to more than one description.

Hypothesis testing Determines the likelihood that a sample statistic could have been selected, if an assumption regarding the population parameter is true Makes inferences about larger populations by comparing calculated values to critical values Confidence interval Determines the likelihood that a population mean falls within a probabilistic range of values Control charts Compares sample data points with specific upper and lower limits to determine process behavior over time

Match the three types of tools to the descriptions of their uses. Some tools may match to more than one description.

Hypothesis testing Used to test an assumption about a population parameter based on a sample statistic Confidence interval Uses a probability percentage for quantifying the uncertainty of its inference about a range value of a population parameter Used to determine the probability that a population mean falls within a certain range of values Control charts Used to plot sample data points to determine whether the process is running within a certain upper and lower limit

Match each type of statistic with the statements that apply to it. Statistics may match to more than one statement

Inferential Work out population characteristics from sample data to predict future outcomes Include hypothesis testing, confidence interval, and correlation tools Descriptive Use techniques such as bar charts, histograms, and measures of central tendency and dispersion Summarize a given dataset

What is the definition of central tendency?

The clustering of values around the mathematical mean

What is the correct definition of the concept of dispersion?

The degree to which data points stray from the central point

What is the definition of dispersion?

The degree to which data spreads out from the mean value

What effects do outliers have on measures of central tendency and dispersion?

The mean value and the standard deviation become unreliable The median may become a better measure of central tendency than the mean

What is the measure of central tendency?

The mean value of a dataset

How do outliers affect measures of central tendency and dispersion?

They inflate the mean value and the standard deviation The mode may become useless as a measure of central tendency