Descriptive Statistics and Law of Large Numbers

Question 1

If we want to represent an entire distribution or at least some special characteristic of it, by means of a single, summary numerical index or a pair of such indices, what is this called?

Answer 1

Descriptive Statistics

Question 2

What is the two major categories of summary statistics (descriptive statistics)?

Answer 2

1. Indices of location 2, Indices of dispersion

Question 3

Indices where some nameable part of a distribution is on the horizontal axis are?

Answer 3

Indices of location

Question 4

This tells us how spread out the distribution is according to some criterion

Answer 4

Indices of dispersion

Question 5

What is another term for regularity?

Answer 5

The mean

Question 6

What is another term for diversity?

Answer 6

Variance

Question 7

What is statistically described via regularity?

Answer 7

– pattern, consistency, shape
– regularity allows for existence of science
– measures of central tendency or location

Question 8

What is statisically described by diversity?

Answer 8

– differences, uniqueness, individuality
– diversity makes for interesting science
– measures of dispersion

Question 9

What are the different types of indicies of location?

Answer 9

1. Mode
2. Median
3. Mean

Question 10

What is the crudest index of location?

Answer 10

Mode

Question 11

Define the mode?

Answer 11

the value that occurs with the greatest
frequency.

In other words, the value that is
possessed by the greatest number of units
in the set.

Question 12

If a data set has two or more values may be tied for the
greatest frequency, what is this called?

Answer 12

Biomodal (2)

Multimodal (2+)

Question 13

What is the value of the middle unit?

Answer 13

Median

Question 14

How do we define the median?

Answer 14

N units arranged in a line in order
of increasing value, the median is the middle one between the highest and lowest value

note that this is unit middle NOT value

Question 15

How do we calculate the median if we have an even # of units in a data set?

Answer 15

Average the 2 middle values

Question 16

What is the 50th percentile?

Answer 16

Median

Question 17

How do we determine a percentile value rank given a data set?

i.e. we are given the data set and the percentile and we are trying to find the value that corresponds to the percentile

THIS IS A BONUS QUESTION NOT COVERED IN THE LECTURE

Answer 17

Question 18

Given a score and a data set how do we determine the percentile rank of a score?

THIS IS A BONUS QUESTION NOT COVERED IN THE LECTURE

Answer 18

Question 19

The best known index of location is….?

Answer 19

THE MEAN

Question 20

What is the formula for the mean?

Answer 20

Question 21

Which index of location is sensitive to extreme score?

Answer 21

The mean

Question 22

What are positive attributes of the mean?

Answer 22

1. IT is the LEAST subject to sampling variation!
2. It IS SENSITIVE TO the exact value of all the scores in the distribution
3. mathematically tractable
4. It is the best guess for the value of any unit drawn at random from a distribution.
   
   • this depends on the types of units being selected

Question 23

Define this term?

Answer 23

The deviation score

(which is the ammount that event x deviates from the mean–x with a line over the top)

Question 24

What is the squared deviation score?

Answer 24

Question 25

Why do we square the deviation score?

Answer 25

Because we want a postive number (sometimes it can be negative if the value is less than the mean)

Question 26

What does this equation define?

Answer 26

The sum of the squared deviation scores OTHERWISE KNOWN AS sum of squares

Question 27

1. What is the sum of the deviations about the mean equal to? 2. Always or just some of the time? 3. Why?

Answer 27

1. 0 2. ALL of the time 3. Because each deviation above the mean is canceled out by a deviation below the mean. This always ends up at zero because the mean is the "center of gravity" or "balance point" of the data set.

Question 28

The sum of the squared devations is a?

Answer 28

A minimum

Question 29

Variance is?

Answer 29

Average squared deviation from the mean

Question 30

What is the most common index of dispersion?

Answer 30

The Variance \*sigh\* again

Question 31

What is the square root of the variance?

Answer 31

Standard deviation

Question 32

What are common indicies of dispersion?

Answer 32

Range Variance Standard Deviation

Question 33

Range is defined as?

Answer 33

The difference between the higest and lowest values Range = High - Low

Question 34

What is the simplest index of dispersion?

Answer 34

The Range

Question 35

According to Goldsmith what is the single most important concept in behavioral statistics? Also, which type is good and bad?

Answer 35

Variance Good variance -- the difference between independent variables--seek to maximize this (inter-group variance) Bad variance -- the differnce between members of each variable--seek to minimize this (intra-group variance)

Question 36

The following are what? * the variance of a random variable is a measure of its statistical * dispersion, indicating how far from the expected value its values * typically are * – a measure of the variation shown by a set of observations defined by * the sum of the squares of deviations from the mean, divided by the * number of degrees of freedom in the set of observations * – a measure of the spread of the values in a distribution * – a measure of variability * – deviation from a standard or norm * – the square of the standard deviation * – a measure of the spread or dispersion of a variable about its mean * – the variance of a real-valued random variable is its second central * moment

Answer 36

Some definitions of variance

Question 37

Which defintion is a very important concept to understand?

Answer 37

– the variance of a real-valued random variable is its second central moment

Question 38

What is the advantage of the standard deviation? Compared to what?

Answer 38

The values are expressed in the orginal units of measurment. As opposed to the variance which does not express them in the orginal values of measurment (because the values are squared)

Question 39

In most other respects which measure of dispersion is more advantageous?

Answer 39

The variance

Question 40

What is the formula for variance?

Answer 40

Question 41

What is this an example of?

Answer 41

Variance of a theoretical distribution

Question 42

What are the properties of variance?

Answer 42

* gives us a measure of dispersion relative to * the mean * sensitive to each score in the distribution * stable with regard to sampling fluctuations * mathematically tractable * variance is directly proportional to the average * squared deviation between all pairs of * observations

Question 43

What does this formual signify?

Answer 43

variance is directly proportional to the average squared deviation between all pairs of observations

Question 44

How do we seperate population variance and sample variance? Why do we do this?

Answer 44

Via two slighlty different formulas

Question 45

Is variance change with respect to location (addition of a constant)?

Answer 45

No it is invariant

Question 46

If you want to multiply some constant to the variance what do you have to do?

Answer 46

You must square the constant.