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intrduction to behavioural statistics

essays- question 3

Variability is the spread of scores around the cental piont. the central piont refers to the middleor mean (average of thre total amout of scores) of the distribution.(Zeisset, 2002). variabilty is

also known as dispersion of scores

(http://www2.le.ac.uk/offices/ld/resources/numeracy/variability). the variability is a way to

connect the mean, median and mode on the same table or graph using the same measuring unit.

variability collects values from abvoe and below the mean. in a normal distribution this is

symetrical. variability decraeses when the population increases. this is becuase the spread is

more compact and there might be little seperations between the scores. with a smaller sample

the ranges might be further apart because the some of the perspectives may not be recognized or

represented. varibilty depends on a number of factors such as, central point, range, standarddeviation (SD), VARIANCE, skeweds, interquatile range and the effects of changing units.

NORMAL DISRIBUTION

in a normal distribution central piont would be at the peak of the curve. this is becuase a normal

distribution the curve is symetrical, bell shaped, and unimodal. therefore since the mean is the

average it should be placed in the centre of the distribution. a normal distribution is necessary

for the representation of all posible scores. this allows for better data intepretation. also levels

less room for unevenness. if for some reaason the distibution of scores tend to pile up on one

side more than onthe other side the distribution is said to be skewed. this can be positively or

negatively. in a posivitely skewed distribution the scores pile up on the positive side of thr

distribution. this maens that the majority of the sample scores were above the maen. therefore

making the population variability positive. in a negatively skewed distribution the scores are

piled up on the negative side of the distribution. this means that the majoity of the spread of

scores are below the mean. then the varibilty of the population is negative. the skewed

distribution can be because the population was to small an gave a bias or one sided response.

this can resultin some of the sample being unrepresented. a larger sample population might be

needed and the variablity will be decreased.

ERROR

the mean is the average and oath to be in the middle then there should be no skewing of the

distribution. skewing the distribution could give the resaerch some extent of biasness. this don't

allow for even variability of the scores. this can creaate either a typeI error or a tpye II error. in a

http://www2.le.ac.uk/offices/ld/resources/numeracy/variabilityhttp://www2.le.ac.uk/offices/ld/resources/numeracy/variabilityhttp://www2.le.ac.uk/offices/ld/resources/numeracy/variabilityhttp://www2.le.ac.uk/offices/ld/resources/numeracy/variability

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type 1 error you are saying that the results are significant when it when really they are due to

chance. for instance you

RANGE

the range is the distance between the lowest and the highest scores in variabilty. since this dealswith extreme (highest and lowest) scores, a small change in the extreme can change the the siz e

of the range. this happens even if the middle has most of the score an d is stable. for example if

you want to make weather predictions the range can tell us what type of weather to posssibliy

expect. the interquatile range(IQR) a tpye of range. it is refered to a maesurement that indicates

the extent to which the central fifty (50%) of within the dataset are dispersed. it's also based and

related to the median. the scores are not counted and are catergorized as bottom twenty-five

percent (25%) and top twenty-five percent (25%). leaving the middle at fifty percent (50%). this

information is according to Zeisset, 2002. in variabilty this is used in calculating abnormal

behaviour. it puts the distribution of the populations behaviour into three (3) section; negativeextreme abnormal~average normal~positive extreme abnormal. at the extreme abnormal

sections the null hypothesis (H0) is rejected. no rejection is needed for normal.

VARIENCE

variance and standard deviantion is coonected. variance is the measure of variablity and all

errors in data. it is based on the deviations from the population mean. standard deviation is the

deviation from the mean, in that you use one to calculate the other and also they are both based

on thi deviations from the mean.standard deviation best used to tabulate variabilty with interval

data. standard deviations can be found by sqauring all the deviantions then adding them up, and

then divding them by the number of deviantion.(SD=Ex2/n). varience is stanard deviation

sqaured(SD2or s

2). the computational formula for varience is (s

2= Ex

2/n-1-(Ex)

2/n/n-1). varience

measure scattered scores or values in a measurement.

in summation is the spread of scores from the maen and as the population or sample gets bigger

the variability gets smaller. this is due to the representation of most of the scores of the sample.

variablity is affected by the range, standard deviation. interqautile range, and varience. a bigger

sample population leaves less room for error.