Find the Q1 of the the following data : 78, 63, 56, 85, 62, 59, 78, 90, 97, 83, 73, 64, 84, 86, 66, 67, 59, 77
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The first quartile (Q1) of a set of data is the data point that divides the set of data into the first 25% versus the last 75% after the dataset has been arranged in order (usually ascending order). This is the data point dividing the first half of a dataset into two equal parts after the dataset is arranged.
Thus, arranging the given data in ascending order, we have 56, 59, 59, 62, 63, 64, 66, 67, 73, 77, 78, 78, 83, 84, 85, 86, 90, 97
There are 18 data points in the dataset, thus there are 9 data points in each half. The first half of the dataset is 56, 59, 59, 62, 63, 64, 66, 67, 73. The halfway (median) is obtained by counting out 4 data points from both ends, which leaves 63 at the center, thus the middle number of the first set is 63 and hence Q1 is 63.