The 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.
What is a quartile of a data set and how is it conceived?
A quartile is a set of values with three points that divides a data set into four equally sized portions. The values that divide a list of numerical data into three quarters are known as quartiles. The center of the three quadrants measures the point of distribution's center and displays data that are close to the center. Only half of the data set is represented by the lower part of the quarters, which is below the median, while the upper section represents the other half, which is above the median. The distribution or dispersion of the data set is shown overall by the quartiles.
When the data points are organized in ascending order, 25% of them are found in the lower quartile, often known as the first quartile (Q1). When presented in increasing order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).
Mathematically, First quartile (Q1) = [(n+1)/4] term
Third quartile (Q3) = [3(n+1)/4] term
The interquartile range is calculated as: Upper Quartile – Lower Quartile = Q3 - Q1
Arranging the given values in ascending order, we have the data set:
40, 42, 46, 47, 51, 55, 58, 67, 67, 68, 69
The total number of terms in the data set = n = 11
Using the formulae established in the literature, we have:
Now, first quartile = Q1 = [(11+1)/4] term = 3rd term = 46
Again, third quartile = Q3 = [3(11+1)/4] term = 9th term = 67
Therefore, interquartile range = Q3 - Q1 = 67 - 46 = 21
Thus, the 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.
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