What is the first quartile and third quartile of the following numbers:
37,42,44, 47,49, 51,53, 54,55, 57,61, 63
Since there are 12 numbers, each quartile must contain 3 numbers.
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To find the first quartile and third quartile of a set of numbers, you need to arrange the numbers in ascending order (from lowest to highest).
The given numbers in ascending order are:
37, 42, 44, 47, 49, 51, 53, 54, 55, 57, 61, 63
First, let's find the first quartile (Q1), which is the median of the lower half of the data set. To do this, divide the data into two halves.
Lower half of the data: 37, 42, 44, 47, 49
Since the number of observations (n) is odd, the median is the middle number. Therefore, Q1 is the median of the lower half, which is 44.
Next, let's find the third quartile (Q3), which is the median of the upper half of the data set.
Upper half of the data: 51, 53, 54, 55, 57, 61, 63
Again, since n is odd, the median of the upper half is the middle number. Therefore, Q3 is the median of the upper half, which is 54.
So, the first quartile (Q1) is 44 and the third quartile (Q3) is 54 for the given set of numbers.