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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.
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
If q1q2q3 are three quartiles then Coefficent of quartile deviation is?
coefficient of quartile deviation is = (q3-q1)/(q3+q1)
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.
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 do you do interquartile range step by step?
Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.
How do you calculate Q1 Q3 and IQR?
to calculate Q1 and Q3, you must first find Q2 - the median. count from wither end of the sample until you find the sole middle number, or find the average of the 2 middle numbers. then, complete the same process to the left of Q2 for Q1, and also on the right for Q3. the IQR is just Q3 - Q1.
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.
What is the formula for coefficient of quartile deviation?
coefficient of quartile deviation: (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
If q1q2q3 are three quartiles then Coefficent of quartile deviation is?
coefficient of quartile deviation is = (q3-q1)/(q3+q1)
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.
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
What is the outlier in 2 3 18 18 18 19 20 20 21 21?
There are no universally agreed determinants are outliers. Commonly used measure are Lower Outer Fence : Q1 - 3*IQR Lower Inner Fence : Q1 - 1.5*IQR Upper Inner Fence : Q3 + 1.5*IQR Upper Outer Fence : Q3 + 3*IQR where Q1 and Q3 are the lower and upper quartiles and IQR = Q3 - Q1. Values further than the outer fence are called extreme outliers while those between the inner and outer fences are mild outliers. On that basis the values 2 and 3 are both mild outliers.
What is the equation of interquartile deviation?
Interquartile deviation Qd=(q3-q1) / 2
Formula of quartile deviation?
Q3-q1
What is math outlier?
There is no standard definition.If Q1 is the lower quartile and Q3 the upper quartile of a set of observations, then the inter quartile range (IQR) is Q3 - Q1.Outliers may be defined as values which are smaller than Q1 - k*(IQR) or larger than Q3 + k*IQR where k is some non-negative real number.
