data analysis :descriptive statistics

Question 1

define descriptive statistics

Answer 1

the use of graphs , tables and summary statistics to identify and analyse sets of data

Question 2

define measures of central tendency

Answer 2

the general term of any measure of the average value in a set of data

Question 3

what are the 3 types of measures of central tendency ?

Answer 3

mean , median and mode

Question 4

how is the mean calculated ?

Answer 4

calculated by adding up all the scores or values in a data set and dividing this figure by the total number of scores there are

Question 5

work out the mean for the following data set of scores :
5 , 7 , 7, 9 , 10 , 11 , 12 , 14 , 15 ,17

Answer 5

total is 107
107/10 the number of scores
mean value of 10.7

Question 6

why is the mean the most sensitive of the measures of central tendency and what does that mean ?

Answer 6

as it includes all of the scores/values in the data set within the calculation
–> this means it is more representative of the data as a whole

Question 7

what is a limitation for mean and give an example of how this could happen ?

Answer 7

it is easily distorted by extreme values
example : if we replace 17 in the data above with the number 98 –> the mean becomes 18.8 which doesn’t really seem to represent the data overall

Question 8

define mean

Answer 8

the arithmetic average calculated by adding up
all the values in a set of data and dividing by the number
of values there are

Question 9

define median

Answer 9

the central value in a set of data when values
are arranged from lowest to highest

Question 10

how is the median calculated ?

Answer 10

the middle value in a data set when scores are arranged from lowest to highest

Question 11

when is the median easily identified ?

Answer 11

in the odd number of scores

Question 12

how is the median identified in the even number of scores ?

Answer 12

the median is halfway between the 2 middle scores

Question 13

what is a strengths for the median ?

Answer 13

• the extreme scores does not effect the result
• it is so easy to calculate

Question 14

what is a limitation for the median ?

Answer 14

it is less sensitive than the mean as not all scores are included in the final calculation

Question 15

what does ‘sensitive’ refer to ?

Answer 15

refers to how easily a measure is influenced by data that’s unusual or doesn’t fit the rest

Question 16

define mode

Answer 16

the most frequently occurring value in a set of
data

Question 17

how to calculate the mode ?

Answer 17

the most frequently occurring score/value within a data set

Question 18

in some sets of data what may there be ?

Answer 18

2 modes - bimodal
OR
no mode if all the scores are different

Question 19

what is limitation of the mode and give an example ?

Answer 19

it is a very crude measure
the mode can
- sometimes be quite different from the mean and the median

Question 20

when would mode be the only method that can be used ?

Answer 20

example :
if you asked your class to list their favourite dessert , the only way to identify the most ‘typical’ or average would be to select the modal group

Question 21

when deciding what method of central tendency should be used what should be considered ?

Answer 21

whether there are any extreme scores

Question 22

what would be best to consider if there is no extreme values and why ?

Answer 22

the mean is the best option as it is
the most sensitive measure of the three

Question 23

what would be best to consider if there is extreme values and why ?

Answer 23

the median is most suitable as the mean
would become distorted

Question 24

what would be never the best option and when would it be appropriate ?

Answer 24

the mode - except if the data are in categories

Question 25

define measures of dispersion

Answer 25

the general term for any measure of the spread or variation in a set of scores

Question 26

what are the 2 examples of measures of dispersion ?

Answer 26

range and standard deviation

Question 27

define the range

Answer 27

a simple calculation of the dispersion in a set of scores which is worked out by subtracting the lowest score from the highest score and adding 1 as a mathematical correction

Question 28

how is the range calculated ?

Answer 28

a simple calculation of the spread of scores and is worked out by taking the lowest value from the highest value and (usually) adding 1

Question 29

why is 1 added when calculating the range and give an example ?

Answer 29

t allows for the fact that raw scores are often rounded up (or down) when they are recorded within research - someone may complete a simple task in 45 seconds - however, it is unlikely they took exactly 45 seconds to complete this task (in fact it may have taken them anywhere between 44.5 and 45.5 seconds), so the addition of 1 accounts for this margin of error

Question 30

what is a strength for the range ?

Answer 30

it is easy to calculate

Question 31

what s a limitation for the range and give an example ?

Answer 31

- it only takes into account for the 2 extreme values --> this may be unrepresentative of the data set as whole EXAMPLE : a student was ill during a test and score 0 and the highest value was a 100 due to the student being given the paper as a homework - this illustrates the problem with range and it may not give a fair representation of the general spread of scores as in this example most students achieved around half marks in the test

Question 32

define standard deviation

Answer 32

a sophisticated measure of dispersion in a set of scores. It tells us how much scores deviate from the mean by calculating the difference between the mean and each score. All the differences are added up and divided by the number of scores. This gives the variance. The standard deviation is the square root of the variance

Question 33

what is the SD considered as ?

Answer 33

much more sophisticated measure of dispersion

Question 34

what does the SD tell us ?

Answer 34

is a single value that tells us how far scores deviate (move away from) the mean

Question 35

the larger the SD

Answer 35

the greater the dispersion or spread within a set of data

Question 36

in a situation where we are talking about a particular condition within an experiment a large SD suggests that ..

Answer 36

that not all participants were affected by the IV in the same way because the data are quite widely spread - may be few anomalous results

Question 37

what may a low SD value reflect ?

Answer 37

the fact that the data are tightly clustered around the mean, --> might imply that all participants responded in a fairly similar way

Question 38

what is a strength of SD ?

Answer 38

much more precise measure of dispersion than the range as it includes all values within the final calculation

Question 39

what is a limitation of SD ?

Answer 39

like the mean – it can be distorted by a single extreme value