Week 1

Question 1

Population

Answer 1

Consists of all the members of a group about which you want to draw a conclusion

Question 2

Sample

Answer 2

The portion of the population selected for analysis

Question 3

Parameter

Answer 3

A numerical measure that describes a characteristic of a population.

Question 4

Statistic

Answer 4

A numerical measure that describes a characteristic of a sample.

Question 5

Descriptive Statistics

Answer 5

Collecting (e.g. survey), summarizing and presenting data (e.g. tables and graphs). Characterize (e.g. sample mean)

Question 6

Inferential Statistics

Answer 6

Drawing conclusions about a population based on sample data (i.e. estimating a parameter based on a statistic).

Question 7

Example of Inferential Statistics

Answer 7

Estimate the population mean weight (parameter) using the sample mean (statistic).

Hypothesis testing - e.g. Test the claim that the population mean weight is 100 pounds.

Question 8

Types of Data

Answer 8

Categorical, Numerical Discrete, Numerical Continuous

Question 9

Categorical Data

Answer 9

Simply classifies data into categories (e.g. marital status, hair color, gender)

Question 10

Numerical Discrete

Answer 10

Counted items - finite number of items (e.g. number of children, number of people who have type-O blood)

Question 11

Numerical Continuous

Answer 11

Measured characteristics - infinite number of items (e.g. weight, height)

Question 12

Levels of Measurement and Measurement Scales

Answer 12

Highest level - Ratio Data
*Differences between measurements, true zero exists (Height, weight, age, weekly food spending)

Interval Data
*Differences between measurements but no true zero (temperature in Celsius, standardized exam scores)

Ordinal Data
*Ordered categories (rankings, order or scaling - tournament rankings, student letter grades, Likert scales)

Lowest level - Nominal Data
*Categories (no ordering or direction - marital status, type of car owned, gender, hair color)

Question 13

Categorical Data (tables and charts)

Answer 13

Summary table
Graphing data -bar charts, pie charts

Question 14

Numerical Data (tables and charts)

Answer 14

Ordered array, stem and leaf display, histogram, frequency and cumulative distributions

Question 15

Examples of describing central tendency

Answer 15

Mean, Median, Mode, Geometric mean

Question 16

Examples of describing variation

Answer 16

range, interquartile range, variance, standard deviation, coefficient of variation

Question 17

Examples of describing shape

Answer 17

Skewness

Question 18

Median

Answer 18

Main advantage over mean is that it is not affected by extreme values

Question 19

Mode

Answer 19

• Not affected by extreme values
• Unlike for mean and median, there may be no unique (single) mode for a given
  data set
• Used for either numerical or categorical (nominal) data
• least least of the 3

Question 20

Mean

Answer 20

Generally used most often, unless extreme (outliers) exist.

Question 21

Quartiles

Answer 21

Split the ranked data into four segments, with an equal number of values per segement

Question 22

The first quartile (Q1)

Answer 22

The value for which 25% of the observations are smaller and 75% are larger.

Q1 position = (n+1)/4

Question 23

The second quartile (Q2)

Answer 23

Q2 is the same as the median (50% are smaller, 50% are larger)
Q2 position =(n+1)/2 (median)

Question 24

The third quartile (Q3)

Answer 24

Only 25% of the observations are greater than the third quartile.

Q3 position = 3(n+1)/4

Question 25

Measures of variation

Answer 25

give information on the spread or variability of the data values

Question 26

Range

Answer 26

Simplest measure of variation
Disadvantages - ignores the distribution of the data, it is sensitive to outliers

Question 27

Interquartile Range (IQR)

Answer 27

Like the median and Q1 and Q2, the IQR is a resistant summary
measure (resistant to the presence of extreme values)

• Eliminates outlier problems by using the interquartile range, as
  high- and low-valued observations are removed from calculations
• IQR = 3rd quartile – 1st quartile

Question 28

Sample Variance (S^2)

Answer 28

Measures average scatter around the mean, units are also squared

Question 29

Sample Standard Deviation - S

Answer 29

Most commonly used measure of variation, shows variation about the mean, has the same units as the original data

Question 30

Variance and Standard deviation - Advantages

Answer 30

-Each value in the data set is used in the calculation
* Values far from the mean are given extra weight as deviations
from the mean are squared

Question 31

Variance and Standard deviation - Disadvantages

Answer 31

Sensitive to extreme values (outliers)
* Measures of absolute variation not relative variation

Question 32

The Z Score

Answer 32

The difference between a given observation and the mean, divided by the standard deviation

A z score above 3.0 or below -3.0 is considered an outlier

Question 33

Shape of a Distribution

Answer 33

Describes how data are distributed
-Left-skewed
-Symmetric
-Right-skewed

Question 34

Population summary measures

Answer 34

Parameters
The population mean is the sum of the values in the population divided by the population size, N

Question 35

Population Variance

Answer 35

The average of the squared deviations of values from the mean

Question 36

Population Standard Deviation

Answer 36

Shows variation around the mean
-the square root of the population variance
-has the same units as the original data

Question 37

The Empirical Rule

Answer 37

If the data distribution is approximately bell-shaped,
then the interval u+-1o contains about 68% of
the values in the population

u+-2o = contains about 95% of the values in the population

u+-3o = contains about 99.7% of the values in the population

Question 38

Determining Outliers

Answer 38

Using the empirical rule
-over or under (1% extreme values) u+-3o

Using Z scores
-above 3 or below -3

Question 39

Exploratory Data Analysis - Box-and-Whisker Plot

Answer 39

A graphical display of data using the 5 number summary
-can determine skewness