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And if this was your homework assignment, you're welcome.....
Well the simple way is to use our five number summary calculator. But if you're doing this by hand...
See list sorting exercise above (rank observations by value). Count the total number of records. Divide by 4. That is the observation in the list for the 25th percentile (Q1, the 1st quartile). Multiply this amount by 3. That is the observation in the list for the 75th percentile (the start of the upper quartile or the top of the 3rd quartile). Anything outside of that range is an outlier.
If an observation falls between two points, the general convention is to average the points. There are more complicated approaches (a weighted average) but this usually will suffice.
The second quartile is the gap between the 25th percentile and the median. The fourth quartile is the gap between the 75th percentile and the maximum value. This captures your interquartile distance.
You can identify the upper half and lower half of a distribution using the smallest value, middle value, and largest value of the sample. This approach is independent of sample size.
The five number summary can be used to create a box plot graph. The range of the graph is denoted as the top of the first quartile and the top of the third quartile. You are treating the upper quartile and lower quartile as outlier data points. The quartile value is used to show the range of the quartile. The whisker diagram shows the range between the extreme values (maximum value, minimum value) of the data.
There is another form of the boxplot referred to as a modified box plot. This adjusts the box and whisker plot so to drop outlier data value points. This site uses a histogram to as a descriptive statistic tool; we can add a modified boxplot if there's sufficient demand.While the five number summary is a good basic measure of a distribution, it doesn't show a full view of the standard deviation, mean, or variance. You need to carefully manage any suspected outlier data points.
You can use the information from the 5 number summary calculator to calculate this. The upper and lower fences are a simple estimate of the potential outliers of a distribution. This approach uses the interquartile range (Q3 - Q1 values) to assess how far outliers may exist. The inner fence is 1.5 x the interquartile range above / below the 1st and 3rd quartiles (respectively). The outer fence is 3.0 x the interquartile range. Note that the lower bounds of these ranges can be a negative number (if the IQR is wide and the absolute values of the first quartile are small. This is common in many logistics problems. In most cases, the underlying data isn't from a normal distribution.
That's how some people refer to the first quartile. This is the bottom of your frequency distribution.