Using the Normal Model

Question 1

How do you standardise a value?

Answer 1

TO standardise a value, we subtract the mean and then divide this difference by the standard deviation.

Question 2

Whar does the letter ‘Z” denote?

Answer 2

The letter Z denotes values that have been standardised.

Question 3

What happens to the measures of position when we shift data?

Answer 3

When we shift data by adding (or subtracting) a constant to each value, all measures of position (centre, percentiles, min, max) will increase (or decrease) by the same constant.

Question 4

What happens to the spread when we shift the data?

Answer 4

Adding (or subtracting) a constant to every data value adds (or subtracts) the same constant to measures of position, bu leaves measures of spread unchanged.

Question 5

What happens to the data when we miltuply or divide values by any constant?

Answer 5

When we multiply or divide all the data values by any constant, all measures of position (such as the mean, median, and percentiles) and measures of spread (such as the range, the IQR, and the standard deviation) are multiplied (or divided) by that same constant.

Question 6

What does standarising into z-scores do to the shape?

Answer 6

Standarising into z-scores does not change the shape of the distribution of a variable.

Question 7

What does standardising into z-scores do to the centre?

Answer 7

Standardising into z-scoares changes the centre by making the mean 0.

Question 8

What does standardisation do to the spread?

Answer 8

Standardisation into z-scores changes the spread by making the standard deviation 1.

Question 9

What is the 68-95-99.7 rule?

Answer 9

In a normal model, about 68% of the values fall within 1 standard deviation of the mean, about 95% of values fall within 2 standard deviations of the mean, and about 99.7% of all the values fall within 3 standard deviations of the mean.

Question 10

What is standardisation?

Answer 10

We standardise to eliminate units. Standardised values can be compared and combined even if the original variables had differnt units and magnitudes.

Question 11

What is a standardised value?

Answer 11

A value found by subtracting the mean and dividing by the standard deviation.

Question 12

What is shifting?

Answer 12

Adding a constant to each data value adds the same constant to the mean, the median, and the quartiles, but does not change the standard deviation or IQR.

Question 13

What is rescaling?

Answer 13

Rescaling is multiplying each data value by a constant multiplies both the measures of position (mean, median and quartiles) and th measures of spread (standard deviation and IQR) by that constant.

Question 14

What is a normal model?

Answer 14

A useful family of models for unimodal, symmetric distributions.

Question 15

What is a parameter?

Answer 15

A numerically valued attribute of a model. For exampke the vlues of μ and σ in a N(μ, σ) model are parameters.

Question 16

What is a statisitc?

Answer 16

A value calculated from data to summarise aspects of the data. for example the mean and standard deviation are statistics.

Question 17

What is a z-score?

Answer 17

A z-score tells how many standard deviations a value is from the mean. Z-scores have a mean of 0 and a standard deviation of 1

Question 18

What is a standard normal model?

Answer 18

A normal model N(μ,σ) with mean μ=0 and standard devitation σ=1. Also called the standard Normal distribution.

Question 19

What is a nearly normal condition?

Answer 19

A distribution is nearly Normal if it is unimodal and symmetric. (We can check by looking at a histogram or a Normal probablility plot.)

Question 20

What is the Normal percentile?

Answer 20

The normal percentile corresponding to a z-score gieves the percentage of values in a standard Normal distribution found at that z-score or below.

Question 21

What is a normal probability plot?

Answer 21

A display to help assess whether a distribution of data is approximately Normal. If the plot is nearly staight, the data satisfy the Nearly Normal Condition.