In the data set below, what is the upper quartile?
3 3 5 7 9
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The upper quartile in this data set is 7.
In the data set below, what is the lower quartile?
15 40 60 83 86 86 96
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The lower quartile in this data set is 40.
To find the upper quartile in a dataset, you need to follow these steps:
Step 1: Sort the data set in ascending order.
In this case, the given data set is already sorted in ascending order: 3 3 5 7 9.
Step 2: Determine the position of the upper quartile.
The upper quartile represents the 75th percentile of the data set, meaning it divides the data into two parts where 75% of the values are less than or equal to the upper quartile. To find the position of the upper quartile, use the formula:
Position = (75/100) × (N + 1)
where N is the total number of data points.
In this case, N = 5, so the position of the upper quartile is:
Position = (75/100) × (5 + 1) = 4th position.
Step 3: Find the value at the determined position.
Since the data set is already sorted, the fourth value in the data set is the upper quartile.
So, in the given data set, the upper quartile is 7.