Measures of Dispersion. Flashcards

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1
Q

The mean can be misleading without some knowledge of _________.

A

Spread. (Dispersion).

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2
Q

What is the simplest way to measure the variation among a set of values?

A

The Range.

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3
Q

What is the range?

A

The distance between the top and bottom values in a data set. (subtract top value from bottom)

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4
Q

What is the most important measure of dispersion?

A

Standard Deviation.

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5
Q

What are the pros of finding the range?

A
  • Includes extreme values

- Easy to calculate.

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6
Q

What are the cons of the range?

A
  • Can be misleading as can be distorted by extreme values

- Not representative of any features of the values between the extremes.

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7
Q

What is distribution?

A

The spread of data.

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8
Q

Why is the interquartile and semi-interquartile range better the range?

A

It is more representative of features of the distribution of values between the extreme’s.

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9
Q

The interquartile and semi-interquartile range focuses specifically on what?

A

On the Central grouping of values in a set.

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10
Q

The ________ range represents the distance between the 2 values that cut off the bottom and top 25% of values.

A

Inter-Quartile.

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11
Q

0.25 x (N+1) - what is this the formula for?

A

To find the position of Q1 (25% / bottom quarter).

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12
Q

0.75 x (N+1) - what is this the formula for?

A

To find the position of Q3 (75 % / top quarter).

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13
Q

After the quartile positions have been identified, what is done?

A

Q3 - Q1 = interquartile range.

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14
Q

What is the formula to find out the interquartile range?

A

Q3 - Q1

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15
Q

What is the semi-interquartile range?

A

Half of the interquartile range.

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16
Q

Q1 and Q3 are the values cutting off the bottom and top ____ of values.

A

25%.

17
Q

Name a pro of the interquartile (and semi-interquartile) range.

A

It is representative of the central grouping of values in a dataset.

18
Q

Name a con of the interquartile (and semi-interquartile) range.

A

It takes no account of extreme values.

19
Q

Name this:

The difference between a number in a data set and the mean.

A

Mean Deviation.

20
Q

If the mean deviation is above the mean, the value is __________.

A

Positive.

21
Q

If the mean deviation is below the mean, the value is __________.

A

Negative.

22
Q

How is the mean deviation calculated?

A

x - x bar

aka. number in data set - mean.

23
Q

What is standard deviation?

A

A calculation of the mean of all deviation values in a dataset to summarise dispersion in terms of deviation from the mean.

24
Q

_____ _______ calculates variance.

A

Standard Deviation.

25
Q

What is standard deviation known to be?

A

The most powerful way to measure spread.

26
Q

In standard deviation, how do we get rid of the negative (sometimes the mean deviations are negative)?

A

We Square the mean deviation.

27
Q

Standard Deviation calculates the ______ amount by which scores differ from the _______.

A

Average, mean.

28
Q

What is the most accurate way of measuring dispersion from the mean?

A

Standard Deviation.

29
Q

What are the steps of standard deviation?

A
  1. Find the mean
  2. Take each deviation value ( x - x bar)
  3. Square this value
  4. Add all squares up
  5. Divide by N-1
  6. Take the square root of this sum.
30
Q

What are the pros of standard deviation?

A
  • Takes exact count of all values

- The most sensitive measure

31
Q

What are the cons of standard deviation?

A
  • Hassle to work out

- It can still be distorted by extreme values.

32
Q

Name the 3 dispersion measures.

A

-The Range
The interquartile and semi-interquartile range
-Standard Deviation.

33
Q

What is the problem with mean deviation?

A

Often we get 0 because it takes negatives into account.

34
Q

What data is standard deviation most appropriate for?

A

Interval data and ratio data.

35
Q

The standard deviation is associated with the mean. But what do we need to take into account?

A

Skew of data.

36
Q

What measure of dispersion should be used for ordinal data?

A

Interquartile Range and Semi-Interquartile Range.

37
Q

If data is nominal what does not apply at all?

A

Dispersion doesn’t apply at all (aka we don’t measure dispersion with nominal data).