To determine the lower quartile, also known as Q1, you must first arrange your data in ascending order and then identify the 25th percentile.
The lower quartile, or Q1, is the value that divides the lowest 25% of the data from the remaining 75%. The initial step is to sort your data set from the smallest to the largest value. This organization is essential because quartiles depend on the specific positions of the data points.
After arranging your data, you can find the position of the lower quartile using the formula:
Q1=4(n+1)In this formula, n represents the total number of data points in the set. This equation provides you with the position of the lower quartile within the ordered list. If the resulting position is a whole number, the value at that position is the lower quartile. If the position is not a whole number, interpolation between the two nearest values is necessary.
For instance, consider a data set containing 9 values. To find the position of the lower quartile, calculate:
Q1=4(9+1)=2.5This result indicates that the lower quartile lies halfway between the 2nd and 3rd values in your ordered list. If the 2nd value is 4 and the 3rd value is 6, you would calculate the lower quartile as follows:
Q1=4+0.5×(6−4)=5Grasping how to find the lower quartile is fundamental for analyzing the distribution and spread of your data, which is a crucial skill in GCSE Mathematics.
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