descriptive stastictics

• meaures of central tendency are averages which give researchers information about the most typical values in a set of data. there are three to consider; mean, mode and median
• the mean is calculated by adding up all the values in a set of data and dividing by the total number of values. the mean is the most senstive of the measures of central tendency as it includes all of the values in a data set within the calculation. this means it is more representative of the data as a whole. however, the mean is easily disorted by extreme values
• the median is the middle value in a data set when scores are arranged from lowest to highest. in an odd number of scores, the median is easily identified. in an even number of scores the median is halfway between the two middle scores. the strength of the median is that extreme scores do not affect it. it is also easy to calculate. however, it is less sensitive than the mean as not all scores are included in the final calculation
• the mode is the most frequently occuring value within a data set. in some data sets, there may be two modes (bi modal) or no mode if all the scores are different. although the mode is very easy to calculate, it is a very crude measure as the mode can be very different from both the mean and median meaning it may not be representative. however, data in categories is when the mode is the only method that can be used. for example, if you asked a class to list their favourite colour, the only way to identify the average would be to select the modal group
• measures of dispersion are based on the spread of values which is how far scores vary from one another. the main focus is the range and the standard deviation
• the range is a simple calculation of the spread of scores and is worked out by taking the lowest value from the highest value and sometimes adding 1. (biggest - smallest) +1. adding 1 is a mathematical correction that allows for the fact that raw scores are usually rounded up when they are recorded within research. e.g. if someone took 45 seconds doing a task they may not have been exactly 45 seconds as it could have been 44.5 or 45.5 so the addition of 1 overcomes this margin of error
• one strength of the range is that it is easy to calculate. however, it only takes into account the two most extreme values and this may be unrepresentative of the data set as a whole.
• the standard deviation is a single value that tells us how far scores deviate (move away from) the mean. the larger the standard deviation, the greater the dispersion within a set of data. if researchers are talking about a condition within an experiment, a large standard deviation suggests that not all participants were affected by the IV in the same way as the data is widley spread. there may be few anomalous results. a low SD reflects that the data is tightly clustered around the mean which could imply all participants responded in a similar way
• the standard deviation is more precise measure of dipersion as it includes all values within the final calculation. however, for the reason, it can be disorted easily by a single extreme value
• to work out the standard deviation we must: For each value in the data set (x), subtract the mean (x̄), and then square the result. Then find the sum of all the resulting values. Next, this sum is divided by the number of values in the data set (N), then the square root of the resulting number is found.
• question example for SD: data set; (2,2,4,5,32) 1. the mean (x) is 2+2+4+5+32/ 5 = 9. 2. now we subtract the mean from each value 2-9 =-7, 2-9=-7, 4-9=-7, 5-9=-4, 32-9=23. 3. then square the results -7(-7)= 49, -7(-7)= 49, -5(-5)= 25, -4(-4) = 16, 23(23) =529 4. find the sum of the sqaured values 49 + 49 + 25 + 16 +529 + 668 5. divide this number of values which in this case is 5 668/5= 133.6 6. find the sqaure root: root133.6 = 11.56