Question

4. Given the data set 27, 29, 51, 54, 45, 48, 60, 52, 51, 49, 52, 48, 43, 46, 45, 42, 50, 56, 45 Are there any values that would be considered outliers? Using the IQR, calculate the lower and upper limits (fences), and then identify any data values that would be considered outliers. Potential Outliers

Answer 1

First Quartile (Q₁)= 45.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

27   29   42   43   45   45   45   46   48   48   49   50   51   51   52   52   54   56   60   

So, the bottom half is

27   29   42   43   45   45   45   46   48   

The median of these numbers is 45.

Thired Quartile(Q₃)

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

27   29   42   43   45   45   45   46   48   48   49   50   51   51   52   52   54   56   60   

So, the upper half is

49   50   51   51   52   52   54   56   60   

The median of these numbers is 52.

I) Interquartile Range :Q₃-Q₁=52-45=7

ii) LF = Q1 - 1.5 * IQR = 45 -(1.5*7) = 34.5
UF = Q3 + 1.5 * IQR = 52+(1.5*7) = 62.5

The Lower fence is the "lower limit" and the Upper fence is the "upper limit" of data, and any data lying outside this defined bounds can be considered an outlier.

Outliers are {27, 29}

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