17. Basic Statistics

Question 1

Central Limit Theorem P.282

Answer 1

The distribution of sample averages will tend toward a normal distribution as the sample size, n, approaches infinity.

Question 2

Inferential statistics P.283

Answer 2

Uses sample data to draw statistical conclusions about the population from which the sample was drawn.

Question 3

Confidence Intervals P. 283

Answer 3

Provides boundaries for an unknown parameter of a population with a specified degree of confidence that the parameter falls within the interval.

Question 4

Hypothesis testing P.283

Answer 4

Test of significance and tests whether events occur by chance or not.

Question 5

Descriptive statistics P.284

Answer 5

Collection of tools and techniques for displaying and summarizing data.

Question 6

Three common ways for quantifying the centrality of a population or sample P. 285

Answer 6

1. Mean
2. Median - Middle value of an ordered data set
3. Mode - Most frequently found

Question 7

Useful description statistics P.287

Answer 7

• Kurtosis, measures the degree to which a set of data is peaked or flat.
• Skewness, measures the degree to which a set of data is not symmetrical.
• Maximum
• Minimum
• First quartile (Q1)
• Second quartile (Q2), median
• Third quartile (Q3)
• Fourth quartile (Q4), Maximum value. Not computed
• Interquartile range (IQR) = Q3 - Q1

Question 8

Determining Quartiles P.290

Answer 8

Q1: W= n+1th /4
If not an integer, w is formated as “y.z” where y is an integer and z is the decimal portion of w.
Q1: Xy+z(Xy+1 - Xy)
Xj = jth observation of the ordered list of sample data.

Q3: W=3(n+1th /4)

Question 9

Frequency distribution P.293

Answer 9

A tabular display of data in mutually exclusive and collectively exhaustive classes or intervals that summarized the number of occurrences in each class.

Class / Class Interval (Cell) - range in which data in frequency distribution table are placed or binned
Class limits - upper and lower limit
Class mark - average value of the class limits
Class boundaries - mutually exclusive and adjacent class (one decimal place more than the original raw data and typically ends in 5)

Question 10

Histogram P.297

Answer 10

A pictorial representation of data based on frequency distribution. Histogram need not have equal class widths. 
Adv.- immediate visual feedback.
Dis. - groups data into classes (raw data lost)

Question 11

Histogram Interval calculation P.297

Answer 11

• 2 to the K rule, 2^k > n. n=population, K=first integer value
• Sturges’s formula. K=1+3.3log10n
• Square root rule. K=√n
• Rice’s rule K=2n^1/3

Question 12

Box-and-Whisker Diagrams P. 298

Answer 12

Graphically display of high and low values of the data, quartiles, the median, outliers, and interquartile range.

Question 13

Scatter Diagrams P.301

Answer 13

Plot of two variables, one on the y-axis and the other on the x-axis. Shows visual examination for patterns to determine whether the variables show any relationship.

Question 14

Normal Probability Plots P.303

Answer 14

Use of special paper that random sample fro a normally distributed population would plot as an approximately straight line. AKA Rankit, QQ, Quantile, PP Plots.

Probability = Mean Rank / (N+1)

Question 15

Descriptive (enumerative) Statistics P. 325

Answer 15

Studies use techniques (numerical and graphical) to present data in an understandable format. Summarize the information revealed in a data set.

Question 16

Inferential (anlytical) P.325

Answer 16

Studies analyze data from a sample to infer properties of the population from which the sample was drawn.