find the range, interquartile range and 50th percentile of the following distribution.
20, 28, 10, 20, 19, 30.
I got a range of 20, but I had forget find the remaining part of the question. Pls some one help me.
We can find the interquartile range or IQR in four simple steps:
Order the data from least to greatest.
Find the median (50th percentile).
Calculate the median of both the lower and upper half of the data.
The IQR is the difference between the upper and lower medians.
Please help me I have arranged them in an ascending order ( 10, 19, 20, 28, 30) but I don't know how to do the remaining part of the question.
The median is the middle score. The medians for upper and lower half are 28 and 19 respectively. Take it from there.
To find the range of a distribution, you subtract the smallest value from the largest value. In this case, the smallest value is 10 and the largest value is 30, so the range is 30 - 10 = 20.
To find the interquartile range, you first need to find the first quartile (Q1) and the third quartile (Q3). The 50th percentile corresponds to the median.
Step 1: Sort the data in ascending order: 10, 19, 20, 20, 28, 30.
Step 2: Calculate the median (50th percentile):
Since the data set has an even number of values, you need to find the average of the two middle values, which in this case are 20 and 20. So the median is the average of 20 and 20, which is (20 + 20)/2 = 20.
Step 3: Calculate Q1 (25th percentile):
To find Q1, you need to find the median of the lower half of the data set. In this case, the lower half of the data set is 10, 19, and 20. Sort this subset in ascending order: 10, 19, 20. Since this subset has an odd number of values, the median is the middle value, which is 19. So Q1 is 19.
Step 4: Calculate Q3 (75th percentile):
To find Q3, you need to find the median of the upper half of the data set. In this case, the upper half of the data set is 20, 28, and 30. Sort this subset in ascending order: 20, 28, 30. Since this subset has an odd number of values, the median is the middle value, which is 28. So Q3 is 28.
Step 5: Calculate the interquartile range (IQR):
The IQR is the difference between Q3 and Q1. In this case, IQR = Q3 - Q1 = 28 - 19 = 9.
Therefore, the range is 20, the 50th percentile is 20, and the interquartile range is 9.