Qm - Module 5 - Summary Measures

Front 1

List of types of Summary measures

Back 1

1. Measure of Location
2. Measure of Scatter
3. Shape of data

Front 2

Measures of Location are also know as ...

Back 2

Measures of central tendency.

Front 3

What is the purpose of the Measures of Location

Back 3

To show, in general terms, the size of the data.

Front 4

What is the arithmetic mean?

Back 4

Sum of readings divided by the number of readings

Front 5

What is the median?

Back 5

The middle value of a set of numbers. There is no mathmatical formula.

Front 6

How do you determine median if there is an even number of values?

Back 6

Take the arithmetic mean of the middle two values as the median.

Front 7

What is the Mode?

Back 7

The most frequently occurring value.

Front 8

How are measures of location calculated for grouped or classified data (frequency table)?

Back 8

Each class is represented by its mid-point, which is used for calculating measures of location.

Front 9

How is the median calculated from a frequency table?

Back 9

Use the mid-point of the class in which the middle value occurs.

Front 10

How is the mode determined from a frequency table?

Back 10

Use the mid-point of the class with the highest number of observations.

Front 11

Most meaningful measure of location for: symmetrical, u-shaped and j-shaped distributions?

Back 11

Symmetrical - arithmetic mean
U Shape - modes (2)
J Shape - median

Front 12

What are other uses for Measures of Location?

Back 12

1. Focus for the eye
2. For comparison

Front 13

What are good reasons not to use the Arithmetic Mean as the Measure of Location?

Back 13

1. Distortion of the mean by outliers
2. Distortion of the mean by clusters
3. Error by taking averages of averages

Front 14

What alternatives should be considered for:
a. Distortion by outliers
b. Distortion by clusters
c. Error by average of average

Back 14

a. The median should be considered
b. The mode should be considered
c. Return to definition of average and correct the calculation

Front 15

Define Measures of Scatter.

Back 15

They are a measure of the extent to which the readings are grouped closely together or are scattered over a wide interval.

Front 16

Measures of Scatter are also known as…

Back 16

Measures of dispersion

Front 17

List the Measures of Scatter.

Back 17

1. Range
2. Interquartile Range
3. Mean Absolute Deviation
4. Variance
5. Standard Deviation

Front 18

Explain Range

Back 18

total interval covered by the numbers

Front 19

Explain Interquartile Range

Back 19

The range of the numbers after having eliminated the highest and lowest 25%.

Front 20

Mean Absolute Deviation

Back 20

is the sum of the absolute difference between each reading and mean divided by the number of readings

Front 21

Variance

Back 21

Sum of squares of deviations of each reading from the mean divided by the number of readings minus 1.

Front 22

Standard Deviation

Back 22

The square root of the Variance

Front 23

Calculation of measures of dispersion

Back 23

1. Calculator
2. Spreadsheet
3. Shortcut formula for calculating Variance

Front 24

Pros and cons of Range

Back 24

Advantage - Easily understood and familiar

Disadvantage - Distorted by outliers; descriptive only

Front 25

Pros and cons of Interquartile Range

Back 25

Advantage - Easily understood

Disadvantage - Not well known; descriptive only

Front 26

Pros and cons of Mean absolute deviation

Back 26

Advantage - Intuitively sensible

Disadvantage - Unfamiliar; mathematically difficult

Front 27

Pros and cons of Variance

Back 27

Advantage - Easy math; used in other theories

Disadvantage - Wrong units; No intuitive appeal

Front 28

Standard Deviation

Back 28

Advantage - Easy math; used in other theories

Disadvantage - Too involved for descriptive purposes

Front 29

How is the method of calculation for the measure of scatter selected?

Back 29

If for purely descriptive - MAD is probably best.
If measure of scatter needed for wider financial or statistical theory, then variance and standard deviation commonly used.

Front 30

Define Coefficient of Variation

Back 30

Standardizes the standard deviation so that comparisons can be made.

Front 31

Formula for Coefficient of Variation

Back 31

Standard deviation divided by the arithmetic mean.

Front 32

What other Summary Measures are occasionally encountered?

Back 32

Skew and Kurtosis

Front 33

Define skew

Back 33

measures the extent to which a distribution is non-symmetrical

Front 34

Explain:
Left Skew
Zero Skew
Right Skew

Back 34

Left Skew (Negatively skewed) - hump is leaning to the right.
Zero Skew - distribution is symmetrical
Right Skew (Positively skewed) - hump is leaning to the left.

Front 35

Define Kurtosis

Back 35

A generally qualitative approach to the degree to which the distribution is 'punched in' or 'filled out'

Front 36

Explain shape of;
low kurtosis
medium kurtosis
high kurtosis

Back 36

Low kurtosis - upside down funnel
Medium kurtosis - upside down 'V'
High kurtosis - upside down 'U'

Front 37

Options in dealing with Outliers

Back 37

1. Twyman's Law - data that looks unusual or interesting is wrong. Check for typo or other error in data.
2. Part of the pattern - should not change or exclude
3. Isolated event - not error, but unlikely to be repeated (not part of the pattern) - usually exclude

Front 38

Procedure for outliers

Back 38

1. Look for mistakes and correct them
2. Decide if part of the pattern or not - to include or exclude.

Front 39

What is an Index?

Back 39

a measure used to summarize the movement of a variable over time. Makes numbers easier to understand and compare with other series.

Front 40

Best known index

Back 40

Cost of Living Index - cost of many different goods, fuel, transport, etc.

Front 41

What is the index base year?

Back 41

The starting point for the series, when the index was 100.

Front 42

Define Simple Index

Back 42

Result of the conversion of one series of numbers into another based on 100

Front 43

What are limits for index

Back 43

A factor of three before and after the base year.

Front 44

What might happen to the base year in a long series?

Back 44

There may be multiple base years.

Front 45

Define a Simple Aggregate Index

Back 45

An index which is used to summarize several factors.

Front 46

Define a price-relative index

Back 46

to counter the impact that higher numbers have on index versus the lower.

Front 47

Define a Weighted Aggregate Index

Back 47

An aggregate index in which you can assign different weightings to reflect the importance of the various components.

Front 48

Define a Laspeyres Index

Back 48

A Weighted Aggregate Index in which the base month quantities are used for the weighting.

Front 49

What is the major criticism of the Laspeyres Index?

Back 49

The weightings used in the base year may over time become un representative.

Front 50

Alternative to Laspeyres Index.

Back 50

Paasche Index

Front 51

Define the Paasche Index

Back 51

Instead of using base year quantities as weightings, they use the quantities from the most recent month. However, everytime the weightings change, the entire series must be recalculated.

Front 52

Define a fixed weight index

Back 52

weights are from neither the base period nor the most recent. They are from an intermediate period, or from the average of several periods.

Front 53

How and why is economic data sometimes deflated (e.g. GNP)?

Back 53

To deflate the GNP is to manipulate the figures to remove the effect of increasing prices on GNP. Makes seeing the true increase/decrease easier. This is done by dividing the current GNP by the current year Price Index and multiplying by 100. This results in the GNP (real).

Front 54

What are synonyms for model?

Back 54

Pattern or summary

Front 55

What information should be included in the model?

Back 55

1. Number of readings
2. A measure of location
3. A measure of scatter
4. The shape of the distribution