To calculate the upper quartile, we need to follow these steps:

1. Arrange the data in ascending order.


2. Find the median of the entire data set.


3. Find the median of the upper half of the data set (excluding the median).


4. This median is the upper quartile of the data set.

The given data set is: 70, 15, 4, 2, 10, 16, 17, 13, 11, 7

Arranging this data set in ascending order gives us:

2, 4, 7, 10, 11, 13, 15, 16, 17, 70



The median of this data set can be calculated by finding the middle value. As there are 10 values in this data set, the middle value is the average of the 5th and 6th values:

Median = (11 + 13)/2 = 12



The upper half of the data set includes the values above the median. These values are:

15, 16, 17, and 70

Arranging these values in ascending order gives us:

15, 16, 17, 70

The median of this data set can be calculated by finding the middle value. As there are 4 values in this data set, the middle value is the average of the 2nd and 3rd values:

Median of Upper Half = (16 + 17)/2 = 16.5



The median of the upper half of the data set is the upper quartile of the entire data set. Therefore, the upper quartile of this data set is:

Upper Quartile = Median of Upper Half = 16.5

Therefore, the upper quartile of the given data set is 16.5.

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