Answer :
Final answer:
To use the Interquartile Range (IQR) method to identify outliers, you calculate Q1, Q3, and the IQR for the data set, then find the lower and upper fences. Values beyond these fences are outliers. In the given data set, 66 and 84 are the outliers.
Explanation:
The Interquartile Range (IQR) is a statistical measure used to identify outliers in a data set. It is calculated by taking the difference between the third quartile (Q3) and first quartile (Q1) values in a set of data. To identify outliers using the IQR, we first need to calculate the Q1, Q3, and IQR for the data set.
For the data set 66, 73, 74, 75, 76, 77, 84: Q1 is 73, Q3 is 77, thus IQR is 4. Next, you calculate the lower and upper fences - values beyond which data is considered to be an outlier. The lower fence is Q1 - 1.5*IQR = 67, and the upper fence is Q3 + 1.5*IQR = 83. Any data points outside these ranges are outliers. So in this data set, 66 and 84 are considered outliers.
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It has been asked to identify outliers in the data set: 84, 75, 77, 66, 73, 76, 74 using the interquartile range (IQR). Let's solve this step by step:
First, order the data set from smallest to largest: 66, 73, 74, 75, 76, 77, 84.
Next identify the median (Q2). Since there are 7 numbers, the median is the 4th number: 75.
Now find the first quartile (Q1), the median of the lower half: (66, 73, 74). The median is 73.
Find the third quartile (Q3), the median of the upper half: (76, 77, 84). The median is 77.
Now calculate the IQR: IQR = Q3 - Q1 = 77 - 73 = 4.
Determine the lower and upper bounds for potential outliers:
Lower Bound = Q1 - 1.5 * IQR = 73 - 6 = 67.
Upper Bound = Q3 + 1.5 * IQR = 77 + 6 = 83.
Next step is to identify any values outside these bounds: 66 is less than 67 and 84 is greater than 83, so 66 and 84 are outliers.
Therefore, 66 and 84 are outliers in this data set.
Hence the answer is 66 and 84
