Descriptive Statistics II

Question 1

What is the Mean?

Answer 1

The (arithmetic) mean – sum the values then divide by the count

Question 2

What is the Median?

Answer 2

The median – order the values then take the midpoint

Question 3

What is the Mode?

Answer 3

The mode – the most common value
(though rarely of practical use for continuous data)

Question 4

What is the mean typically reported with?

Answer 4

Standard Deviation

Question 5

What is the median typically reported with?

Answer 5

Central Range

Question 6

What is Standard Deviation?

Answer 6

describes dispersion of values around the mean

When describing samples the mean is denoted by ¯𝒙 and the SD by s
When describing populations the mean is denoted by µ and the SD by σ

𝑠= √((∑_(𝑖=1)^𝑛▒〖(𝑥_𝑖−¯𝑥)〗^2 )/(𝑛−1))

Question 7

What is the range?

Answer 7

Range – the lowest value and the highest value
(or the distance between them)

Question 8

What are centiles?

Answer 8

Centiles – the median is the 50th centile. We can describe spread using centiles around that, e.g. 5th to 95th gives 90% central range.

Question 9

What are centiles?

Answer 9

Centiles – the median is the 50th centile. We can describe spread using centiles around that, e.g. 5th to 95th gives 90% central range.

Question 10

What is the IQR?

Answer 10

interquartile range (IQR) – the 25th to the 75th centile, which gives the central 50% range.

Question 11

What is Normal Distribution?

Answer 11

If the distribution is Normal, the mean and median will be the same.
Symmetric (mean, median and mode are equal)

Take the property of 95% of values lying within 2 SD of the mean
We can use this to create a 95% reference interval or ‘normal range’
It is a range within which 95% of values fall
Mean ± 2SD
(or mean ± 1.96SD to be more precise)

Question 12

What does the standard deviation give us?

Answer 12

The standard deviation gives us information on the shape of the distribution.

Question 13

What is a parametric statistical model?

Answer 13

Parametric – make distributional assumptions

Question 14

What is a non-parametric statistical model?

Answer 14

Non-parametric – make no assumptions (distribution-free)

Question 15

What is Correlation?

Answer 15

Correlation – a measure of linear relationship between variables
Quantified by the correlation coefficient r
r is bound between -1 and 1
The closer to |1|, the stronger the correlation
The closer to 0, the weaker the correlation
Can be positive (as one variable increases, so does the other)
Or negative (as one variable increases, the other decreases)
The ordering of the variables does not matter

Question 16

Give Examples of Correlation

Answer 16

Positive linear correlation: height and shoe size
No linear correlation: amount of tea consumed and intelligence
Negative linear correlation: time spent running vs body fat

Question 17

What is Correlation Coefficient used to describe?

Answer 17

The correlation coefficient is used to describe linear relationships