Descriptive Statistics

Question 1

What do descriptive statistics include?

Answer 1

Average (mean), mode and median, ranger, interquartile range, standard deviation.

Question 2

What do descriptive statistics measure?

Answer 2

measures of central tendency - a summary of data

Question 3

The mean - how do you work it out?

Answer 3

1. SUM of the values / by how MANY values (N) = the mean

Question 4

With what data would the mean be used?

Answer 4

in RATIO data with SMALL samples.

Large samples need a computer

Question 5

What is the mean strongly affected by and what should be used instead?

Answer 5

Extreme values.

You should use the median because it is less senstitive.

Question 6

The median - how do you work it out?

Answer 6

Put numbers into NUMERICAL order and select central number

If there is an even number of values, you find the mean (or half way point) of two central numbers.

Question 7

what is the median used for?

Answer 7

Ordinal and ratio data

Question 8

What are you trying to find with the median?

Answer 8

The MIDDLE number - RANK is important not absolute value (less affected by extreme values)

Question 9

The mode - how and what are you working out?

Answer 9

The mode is the most frequently occuring value.
NOMINAL data can ONLY use mode out of the desciptive stats.
Mode can be used in ordinal and ratio data as well.

Question 10

The range - what is this and how do you work it out?

Answer 10

• The range is the numerical value of difference between the maxium and minimum values.
• The HIGHEST value - LOWEST value = the range
• It is a simple way of experessing THE SPREAD OF VALUES

Question 11

What is the range sensitive too?

Answer 11

EXTREME VALUES. Instead we use the interquartile range.

Question 12

Interquartile Range - How do you work this out?

Answer 12

Split the data into 4 equal parts (quartiles).

UPPER quartile - LOWER quartile = interquartile range.

Question 13

What other descriptive statistic is the interquartile range used in assosiation with and why.

Answer 13

The median. They have the same principle strategy:

10 12 12 15 16 19 22 23 28 30 31
^ ^ ^
19 = median
12 + 28 = quartiles. (28-12=16 (the int. range)

Question 14

write down the pairs of measures of variability you would report together.

Answer 14

interquartile range + median
Standard Deviation (SD) + mean

Question 15

Standard Deviation (SD) - what is this and what data do you use it on?

Answer 15

• Takes into account ALL data points not select ones.
• calculated from VARIANCE (s2), a measure of variability.
• Used in ratio data
• The LARGER the SD the MORE SPREAD OUT the data is.

Question 16

What symbol can the Sandard Deviation be indicated by?

Answer 16

A greek sigma or s (‘o-‘ a smidge like this)

Question 17

What can the mean be depicted by?

Answer 17

a mu (‘mew’) like this: u

Question 18

What does frequency distribution show us?

Answer 18

the SHAPE of the data through histograms

Question 19

how does normal distribution appear on a histogram?

Answer 19

A bell curve.

Question 20

What information can be taken from looking at a bell curve?

Answer 20

Normal distribution

The central peak is the mean

Question 21

What types of skewed distributions can you get?

Answer 21

Negatively skewed (to the right)
Possitiveky skewed (to the left)
Bimodal (2 peaks or MODES - i.e commonest values)

Question 22

What discriptive statistics would you report when data are skewed?

Answer 22

interquartile range and the median.

Question 23

What descriptive statistics would you report when data are normally distributed?

Answer 23

Mean and SD

Question 24

What statistics would you use on skewed or normal distribution?

Answer 24

skewed - non-parametric)

Normal -parametric (because it assumed the data is normally distributed)