How To Calculate the Upper Quartile of a Dataset in 3 Steps

To calculate the range, you need to find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum). The range only takes into account these two values and ignore the data points between the two extremities of the distribution. Its used as a supplement to other measures, but it is rarely used as the sole measure of dispersion because it’s sensitive to extreme values.

The interquartile range and semi-interquartile range give a better idea of the dispersion of data. To calculate these two measures, you need to know the values of the lower and upper quartiles. The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The median is considered the second quartile (Q2). The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range.

Then, determine how many numbers are in the set. The formula for calculating the upper quartile is Q3 = ¾ (n +1). Q3 is the upper quartile and n is the number of numbers in your data set. For example, if you have 10 numbers in your data set, you would solve Q3 = ¾ (10 + 1), then solve ¾ x 11, which would give you 8 ¼.

Find the Median, Lower Quartile, and Upper Quartile

Why is it important to calculate the upper quartile?

The upper quartile is a useful statistical measurement that provides more information about a dataset. By comparing this number to the lower quartile and median, you can determine how big the spread is and conclude whether the results are skewed. For example, consider a coach who records the following 100-meter sprint times for eight high school football players in seconds: {13.4, 13.6, 14.0, 14.5, 15.2, 16.8, 17.6, 19.1}. A college scout realizes its unfair to compare the sprint time of a lineman to a running back, so they decided to use quartiles to separate the times.

The college scout creates four percentiles with two numbers in each percentile. The lower quartile is 13.8 seconds and separates the first percentile from the second percentile. Similarly, the upper quartile is 17.2 seconds and separates the third percentile from the fourth percentile. Now, the college scout can compare athletes against athletes of similar abilities rather than drawing generalized conclusions about their speed. For instance, consider someone who runs a 17.7-second 100-meter dash. This time might seem slow when you consider the whole dataset, but its one of the fastest times in the fourth percentile.

What does it mean to calculate the upper quartile?

When you calculate the upper quartile, you find the value that separates the upper 25% of the data from the lower 75% of the data. The word quartile refers to the practice of separating a dataset into four sections. The first quartile separates the 25th and 50th percentiles, and the median separates the bottom half of the data from the top half. While the upper quartile, also known as the third quartile, separates the upper 25% from the lower 75% of the data, you can also think of it as separating the third percentile from the fourth percentile.

For instance, consider the following dataset: {6, 6, 7, 7, 8, 8, 9, 10}. You can split the data into four sections that have two numbers each. The value of 8.5 would be the upper quartile, as it indicates that the numbers in the three lower sections are below this number and the numbers in the upper section are above this number.

How to calculate the upper quartile

Heres how to calculate the upper quartile of a dataset:

1. Order your dataset

If your dataset is out of order, its important to organize it in ascending order. Put the smallest number on the left side and end with the largest number on the right side. Place any repeating values next to each other. If your dataset is particularly large, consider using an online number sorter to organize the values in ascending order. For instance, if your dataset is {1, 2, 1, 10, 5, 3, 7, 8}, it would become {1, 1, 2, 3, 5, 7, 8, 10}.

2. Find the median

The median is the middle number in an ascending list of numbers. Calculate the median by crossing off the left-most and right-most numbers. Repeat this process until you reach a single number in the middle. For instance, consider this dataset: {1, 2, 5, 5, 7}. You would begin by crossing off the numbers 1 and 7. Then, you would cross off 2 and the right-most 5. The middle 5 is the only value remaining, making it the median of the dataset.

Its important to recognize that a dataset with an even amount of values seemingly results in two median values. For instance, consider this dataset: {1, 2, 5, 5}. You would cross off 1 and the right-most 5, leaving 2 and 5 as the median values. The next step is to calculate the average of these two median values, which means you add them together and divide by two. Adding the values of 2 and 5 gets you seven, which divided by two is 3.5. This makes 3.5 the true median value of this dataset.

3. Find the median of the upper half of the data set

The upper quartile is essentially the median of the upper half of the data set. By applying step two to the upper half of the data set, you can determine the upper quartile. For instance, consider this dataset: {5, 6, 7, 10, 19, 20, 21}. The value of 10 is the median for the whole dataset, so all the numbers above 10 represent the upper half of the data. You can find the median of {19, 20, 21} by crossing off left and right numbers until you reach the middle value.

In this case, the upper quartile for the entire dataset is 20. Numbers above 20 are in the upper 25% percentile, and numbers below 20 are in the lower 75% percentile. Note that an extra step is necessary if the upper half of the data set has an even number of values. For instance, imagine that the dataset was {5, 6, 7, 10, 10, 19, 20, 21} instead of {5, 6, 7, 10, 19, 20, 21}. The new upper half of the data is {10, 19, 20, 21}, making the upper quartile 19.5 instead of 20.

FAQ

How do u find the upper quartile?

The upper quartile is the median of the upper half of a data set. This is located by dividing the data set with the median and then dividing the upper half that remains with the median again, this median of the upper half being the upper quartile.

How do you find the upper quartile and lower quartile?

The lower quartile is the mean of the values of the data point of rank 6 ÷ 2 = 3 and the data points of rank (6 ÷ 2) + 1 = 4. The result is (15 + 36) ÷ 2 = 25.5. The upper quartile is the mean of the values of data point of rank 6 + 3 = 9 and the data point of rank 6 + 4 = 10, which is (43 + 47) ÷ 2 = 45.

What is an example of upper quartile?

The formula for quartiles is given by:
  1. Lower Quartile (Q1) = (N+1) * 1 / 4.
  2. Middle Quartile (Q2) = (N+1) * 2 / 4.
  3. Upper Quartile (Q3 )= (N+1) * 3 / 4.
  4. Interquartile Range = Q3 – Q1.

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