Find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum) to determine the range. The data points between the distribution’s two extremes are not taken into account by the range; it only considers these two values. Due to its sensitivity to extreme values, it is typically used in conjunction with other measures rather than as the sole indicator of dispersion.
A better understanding of the data’s dispersion can be gained from the interquartile range and semi-interquartile range. You must be aware of the lower and upper quartile values in order to calculate these two measures. When data points are arranged in increasing order, the lower quartile, also known as the first quartile (Q1), is the value below which 25% of the data points are found. When data points are arranged in increasing order, the value below which 75% of them can be found is known as the upper quartile, or third quartile (Q3). The median is considered the second quartile (Q2). The difference between the upper and lower quartiles is known as the interquartile range. The semi-interquartile range is half the interquartile range.
Find the Median, Lower Quartile, and Upper Quartile
Why is it important to calculate the upper quartile?
A useful statistical measurement that reveals more details about a dataset is the upper quartile. You can determine the size of the spread and whether the results are skewed by comparing this number to the lower quartile and median. Consider a coach who keeps track of the sprint times for 100 meters for eight high school football players. 4, 13. 6, 14. 0, 14. 5, 15. 2, 16. 8, 17. 6, 19. 1}. A college scout decided to use quartiles to separate the times because they realized it was unfair to compare a lineman’s sprint time to a running back’s.
The college scout generates four percentiles, each of which contains two numbers. The lower quartile is 13. The first percentile and second percentile are separated by 8 seconds. Similarly, the upper quartile is 17. The third percentile and fourth percentile are separated by 2 seconds. Instead of making assumptions about an athlete’s speed, the college scout can now compare them to athletes of similar abilities. For instance, consider someone who runs a 17. 7-second 100-meter dash. When compared to the entire dataset, this time may appear slow, but it is one of the fastest times in the fourth percentile.
What does it mean to calculate the upper quartile?
The value that divides the upper 25% of the data from the lower 75% of the data is what you find when you calculate the upper quartile. The term “quartile” describes the procedure of dividing a dataset into four parts. The median divides the data into two halves, with the first quartile separating the 25th and 50th percentiles. You can think of the upper quartile as dividing the third percentile from the fourth percentile even though it divides the upper 25% from the lower 75% of the data. The upper quartile is also referred to as the third quartile.
Consider the dataset 6, 6, 7, 7, 8, 8, 9, 10 as an example. The information can be divided into four sections, each with two numbers. The value of 8. The upper quartile would be 5, meaning that all of the numbers in the three lower sections would fall below it while all of the numbers in the upper section would rise above it.
How to calculate the upper quartile
Heres how to calculate the upper quartile of a dataset:
1. Order your dataset
It’s crucial to arrange your dataset in ascending order if it’s out of order. Place the smallest number on the left and the largest number at the end on the right. Place any repeating values next to each other. Consider using an online number sorter to arrange the values in ascending order if your dataset is particularly large. For instance, your dataset would become “1, 1, 2, 3, 5, 7, 8, 10” if it were “1, 2, 1, 10, 5, 3, 7, 8”.
2. Find the median
In an ascending list of numbers, the median is the middle number. Cross off the leftmost and rightmost numbers to calculate the median. Continue doing this until you get to the middle number. For instance, consider this dataset: {1, 2, 5, 5, 7}. You’d start by erasing the numbers 1 and 7. Then, you would cross off 2 and the right-most 5. The dataset’s median is the last remaining value, which is the middle 5 values.
It’s crucial to understand that a dataset with an even number of values appears to have two median values. For instance, consider this dataset: {1, 2, 5, 5}. You would eliminate 1 and the fifth from the right, leaving the median values to be 2 and 5. The average of these two median values must then be determined, which requires adding them together and dividing by two. Two plus five equals seven, which when divided by two equals three. 5. This makes 3. 5 the true median value of this dataset.
3. Find the median of the upper half of the data set
In essence, the upper quartile represents the median of the data set’s upper half. You can determine the upper quartile by applying step two to the data set’s upper half. Take this dataset, for instance: 5, 6, 7, 10, 19, 20, 21 All numbers above 10 represent the upper half of the data because 10 is the median for the entire dataset. By erasing the left and right numbers until you reach the middle number, you can calculate the median of “19, 20, 21”
In this instance, 20 represents the upper quartile for the entire dataset. Numbers below 20 fall into the lower 75% percentile, while those above 20 fall into the upper 25% percentile. Keep in mind that if the data set’s upper half contains an even number of values, an additional step will be required. Consider the dataset to be 5, 6, 7, 10, 10, 19, 20, 21 rather than 5, 6, 7, 10, 19, 20, 21. The updated data’s upper half is now 10, 19, 20, and 21, making the upper quartile 19 5 instead of 20.
FAQ
How do u find the upper quartile?
The median of a data set’s upper half is the upper quartile. The upper quartile is found by first dividing the data set by the median, and then by the remaining upper half, which is divided by the median once more.
How do you find the upper quartile and lower quartile?
The data point of rank 6 2 = 3 and the data point of rank (6 2) + 1 = 4’s mean values make up the lower quartile. The result is (15 + 36) ÷ 2 = 25. 5. The upper quartile is calculated as (43 + 47) 2 = 45, which is the mean of the values of the data points of rank 6 + 3 = 9 and 6 + 4 = 10.
What is an example of upper quartile?
- Lower Quartile (Q1) = (N+1) * 1 / 4.
- Middle Quartile (Q2) = (N+1) * 2 / 4.
- Upper Quartile (Q3 )= (N+1) * 3 / 4.
- Interquartile Range = Q3 – Q1.
