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Suppose there are n observations. Put them in ascending order (smallest first) of size.
Calculate k = n/4. Round up to the next integer, if necessary.
Then Q1 is the kth observation in the ordered sets.
Also Q3 is the 3kth observation in the ordered sets.
IQR = Q3 - Q1
Calculation of the standards deviation is a lot more work.
First find the mean = sum of all the observations, divided by the number of observations. Call that number M.
Next find the mean "sum of squares", MSS. Square the value of each observation and add them together. Then divide this sum by the number of observations.
Then the Variance is V = MSS - M2
Finally, the standard deviation is sqrt(V).
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What are outliers and how do they affect data?
Outliers are observations that are unusually large or unusually small. There is no universally agreed definition but values smaller than Q1 - 1.5*IQR or larger than Q3 + 1.5IQR are normally considered outliers. Q1 and Q3 are the lower and upper quartiles and Q3-Q1 is the inter quartile range, IQR. Outliers distort the mean but cannot affect the median. If it distorts the median, then most of the data are rubbish and the data set should be examined thoroughly. Outliers will distort measures of dispersion, and higher moments, such as the variance, standard deviation, skewness, kurtosis etc but again, will not affect the IQR except in very extreme conditions.
If q1q2q3 are three quartiles then Coefficent of quartile deviation is?
coefficient of quartile deviation is = (q3-q1)/(q3+q1)
How do you calculate an interquartile range with an even number of scores?
If you have 2n scores, then Q1 = (2n+1)/4 Q3 = 3*Q1 In both cases, depending on your level, you take the nearest integer to Q1 and Q3, or you interpolate. If you do not know what interpolate means then you are probably not yet at the necessary level! and IQR = Q3 - Q1
What is an outlier when finding the median?
an outlier can be found with this formula... Q3-Q1= IQR( inner quartile range) IQR*1.5=x x+Q3= anything higher than this # is an outlier Q1-x= anything smaller than this # is an outlier
How does the outlier affect the median of this data?
An outlier is 1.5 times the mean, when you are taking an average it may give an inaccurate representation of the data. It usually does not affect the median.* * * * * The above definition of an outlier is total rubbish! It is necessary to have a measure of the central tendency (mean or median) AND spread (standard deviation or inter quartile range - IQR) to define an outlier.If Q1 and Q3 are the lower and upper quartiles, then outliers are normally defined as observations lying below Q1 - k*IQR or above Q3 + k*IQR. There is no universally agreed definition of outliers and hence no fixed value for k. But k = 1.5 is often used.
