Research produces numerical data, especially during quantitative research. Raw data must be converted into statistics, which provide information.
Descriptive stats only allow us to describe and summarise data.
There are 2 types of summaries of results in descriptive stats: measures of central tendency which give averages; measures of dispersion which look at a spread of the scores.
Central tendency reduces a large set of results to a single value. The 3 measures of central tendency are: mode, median, mean. These are good at summarising data but they don't consider the spread of scores.
Measures of dispersion allow us to examine the variability within our data sets. 2 measures of dispersion are: range and standard deviation
The mean is the average of the data.
to work out the mean all the results are added together then the total of this is divided by the amount of results.
33, 32, 34
advantage: makes use of all the values and so is sensitive measure of central tendency.
disavantages: May produce decimal points for whole numbers, which may be less meaningful (i.e. 2.333. of a person); if one value is extremely high or low compared to the other results may distort the answer.
The mode (modal value) is the value which most often occurs.
5 occurs 4 times
6 occurs 2 times
7 occurs once
4 occurs once
5 is the median in this case
Advantages: Modal value is a figure which actually occurs in the sequence; uneffected by extreme values.
Disadvantages: Not useful in small sets of data or when there are two many modes; tells us nothing about the other values in the set.
The median is the central point/middle point of the data. For to find the median values have to be placed in rank order and then the middle point of this scale of values can be found
There is no one middle value so the two values on either the side of the middle are added together then divided by two to find the middle value.
Advantages: unaffected by extreme values, easier to calculate than mean
Disadvantages: unrepresentative with small data, doesn't take into account the exact values of items
A simple way of measuring the variation amongst a set of values. It is the distance between the smallest and largest value plus 1.
Advantage: Quick and easy to calculate
Disadvantage: Doesn't use all values, seriously effected by outlies
Standard diviation is a statistical measure of variation of a set of scores and tells us how much, on average, scores differ from the mean. A large SD tells us that the scores are spread widely, a small SD that results are less soread out.
work out the average: (2+3+4)/3=3
minus the average from each starting result: 2-3=-1, 3-3=0, 4-3=1
square the last 3 results: 1, 0, 1
add these new results together: 1+1+0=2
subtract 1 from the number of observations in the group: 3-1=2
Divide the sum of the squares by the last value found: 0
square root of last answer: 0/0=0
Advantages: The value of each score is taken into account, it is a most sensitive measure of dispersion,used in advanced statistical procedures.
Disadvantages: complicated to work out