Measures of Dispersion.

Question 1

The mean can be misleading without some knowledge of _________.

Answer 1

Spread. (Dispersion).

Question 2

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

Answer 2

The Range.

Question 3

What is the range?

Answer 3

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

Question 4

What is the most important measure of dispersion?

Answer 4

Standard Deviation.

Question 5

What are the pros of finding the range?

Answer 5

• Includes extreme values

- Easy to calculate.

Question 6

What are the cons of the range?

Answer 6

• Can be misleading as can be distorted by extreme values

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

Question 7

What is distribution?

Answer 7

The spread of data.

Question 8

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

Answer 8

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

Question 9

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

Answer 9

On the Central grouping of values in a set.

Question 10

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

Answer 10

Inter-Quartile.

Question 11

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

Answer 11

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

Question 12

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

Answer 12

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

Question 13

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

Answer 13

Q3 - Q1 = interquartile range.

Question 14

What is the formula to find out the interquartile range?

Answer 14

Q3 - Q1

Question 15

What is the semi-interquartile range?

Answer 15

Half of the interquartile range.

Question 16

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

Answer 16

25%.

Question 17

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

Answer 17

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

Question 18

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

Answer 18

It takes no account of extreme values.

Question 19

Name this:

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

Answer 19

Mean Deviation.

Question 20

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

Answer 20

Positive.

Question 21

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

Answer 21

Negative.

Question 22

How is the mean deviation calculated?

Answer 22

x - x bar

aka. number in data set - mean.

Question 23

What is standard deviation?

Answer 23

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

Question 24

_____ _______ calculates variance.

Answer 24

Standard Deviation.

Question 25

What is standard deviation known to be?

Answer 25

The most powerful way to measure spread.

Question 26

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

Answer 26

We Square the mean deviation.

Question 27

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

Answer 27

Average, mean.

Question 28

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

Answer 28

Standard Deviation.

Question 29

What are the steps of standard deviation?

Answer 29

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.

Question 30

What are the pros of standard deviation?

Answer 30

- Takes exact count of all values | - The most sensitive measure

Question 31

What are the cons of standard deviation?

Answer 31

- Hassle to work out | - It can still be distorted by extreme values.

Question 32

Name the 3 dispersion measures.

Answer 32

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

Question 33

What is the problem with mean deviation?

Answer 33

Often we get 0 because it takes negatives into account.

Question 34

What data is standard deviation most appropriate for?

Answer 34

Interval data and ratio data.

Question 35

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

Answer 35

Skew of data.

Question 36

What measure of dispersion should be used for ordinal data?

Answer 36

Interquartile Range and Semi-Interquartile Range.

Question 37

If data is nominal what does not apply at all?

Answer 37

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