Numerical Descriptive Techniques and Graphical Methods

Question 1

What is the “distribution” of the variable?

Answer 1

• The data we collect when measuring a variable have different values.
• For example, the variable ”weight of adult birds” probably will have different values each island: 670, 345, 563, 1050, 982 grams etc. . .
• This group of different values is collectively referred to as the distribution of the variable.

Question 2

What measurements can be used to describe a variables distribution?

Answer 2

Central tendency
Dispersion
Skewness
Kurtosis

Question 3

What is the central tendency?

Answer 3

A central or typical value for a probability distribution. (Where is the middle)

Question 4

What is the Dispersion?

Answer 4

How spread out is the data?

Question 5

What is the skewness

Answer 5

A measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or undefined.(Is the data ‘skewed’ to left or right?)

Question 6

What is Kurtosis?

Answer 6

A measure of the combined sizes of the two tails. It measures the amount of probability in the tails. (How peaked is the centre?)

Question 7

What are the measures of central location?

Answer 7

• Mean
• Median
• Mode

Question 8

What are the measures of Variability?

Answer 8

• Range
• Standard Deviation
• Variance
• Coefficient of Variation

Question 9

What are the measures of Relative Standing?

Answer 9

• Percentiles

- Quartiles

Question 10

What are the measures of Linear Relationship?

Answer 10

• Covariance
• Correlation
• Determination
• Least Squares Lines

Question 11

What is the median and the mode?

Answer 11

• Median = Midpoint of ranked values
• Mode = Most frequently observed value
• Both are unaffected by outliers

Question 12

What does the symbol “Sigma” mean?

Answer 12

• To sum or add up

Question 13

What is the Arithmetic Mean?

Answer 13

• The most common measure of central tendency (Aka - the mean)
• Commonly called the average
• Calculated as the sum of values divided by the number of values
• Affected by extreme values (outliers)

Question 14

How can you find the median?

Answer 14

• If the number of values in the data set is odd, the median is the middle ranked value
• If the number of values in the data set is even, the median is the mean (average) of the two middle ranked values

Question 15

What are the different types of skewness?

Answer 15

• Symmetrical Distribution
• Negatively Skewed Distribution (Leaning to the right)(Aka Left Skewed)
• Positively Skewed Distribution (Leaning to the left) (Aka Right skewed)

Question 16

Why are Measures of Variation important?

Answer 16

Measures of variation give information on the spread or variability of the data values.

Question 17

If two lines where drawn on a graph with the same mean and one came to an immediate peak where as one had a gradual curve, which would have more variability?

Answer 17

• The line with the gradual curve. This is because an immediate curve would imply that all the observations that were recorded were very close or similar to the mean and so are all in one area, where as, the gradual curve implies that the data was more spread out.

Question 18

What is the Range of a data set?

Answer 18

• The range is the simplest measure of variability, calculated as:
• Range = Largest observation – Smallest observation
• However, It is influenced by outliers

Question 19

Why are Variance and Standard Deviation important in Statistics?

Answer 19

They are used to measure variability, they also play a vital role in almost all statistical inference procedures.

Question 20

What is the population variance denoted by?

Answer 20

Lower case Greek letter “sigma”, squared.

Question 21

What is the sample variance denoted by?

Answer 21

Lower case “s” squared

Question 22

How can you find the standard deviation from the Variance?

Answer 22

• The standard deviation is simply the square root of the variance, thus:
• Population standard deviation: (Lower case Greek letter for “Sigma” squared, in the square root sign)
• Sample standard deviation:(lower case “s” squared in the square root sign)

Question 23

How can we interpret the Standard Deviation?

Answer 23

• The standard deviation can be used to compare the variability of several distributions and make a statement about the general shape of a distribution. If the histogram is bell shaped, we can use the Empirical Rule.

Question 24

What is the Empirical Rule?

Answer 24

• Approximately 68% of all observations fall within one standard deviation of the mean.
• Approximately 95% of all observations fall within two standard deviations of the mean.
• Approximately 99.7% of all observations fall within three standard deviations of the mean.

Question 25

What is the Coefficient of Variation?

Answer 25

• The coefficient of variation of a set of observations is the standard deviation of the observations divided by their mean
• This coefficient provides a
  proportionate measure of variation

Question 26

What are Quartiles?

Answer 26

• They are the 25th, 50th and 75th percentiles of data
• The first or lower quartile is labeled Q1 = 25th percentile.
• The second quartile, Q2 = 50th percentile (which is also the median).
• The third or upper quartile, Q3 = 75th percentile.

Question 27

Where are the Quartiles used?

Answer 27

• In a Box-and-Whisker Plot: A graphical display of data using a %-number summary:
• Min, Q1, Median, Q3, Max
• A Box-and-Whisker Plot can be both horizontal or Vertical

Question 28

What is the Interquartile Range?

Answer 28

• Interquartile Range = Q3 – Q1
• The interquartile range measures the spread of the middle 50% of the observations.
• Large values of this statistic mean that the 1st and 3rd quartiles are far apart indicating a high level of variability.

Question 29

What are the different graphics commonly used in statistics?

Answer 29

• Bar Chart
• Clustered Bar Chart
• Pie Chart
• Box and whisker plot
• Q-Q Plot
• Scatter Plot