The following are responses to a graduate survey on the salaries offered to Bachelor of Business graduates (in $ thous).45.0 42.1 29.9 22.3 35.6 23.9 27.8 40.5 25.9 26.6 33.0 29.2 37.0 20.8 24.4 43.2The first quartile for this data set is _______ $thous. (2 dec pl)

Question

BlackTom AI · Accepted Answer

We start by listing all observations from the survey data to compute the first quartile.
The data values are (in thousands): 45.0, 42.1, 29.9, 22.3, 35.6, 23.9, 27.8, 40.5, 25.9, 26.6, 33.0, 29.2, 37.0, 20.8, 24.4, 43.2.
Next, sort the data from smallest to largest to see the order clearly: 20.8, 22.3, 23.9, 24.4, 25.9, 26.6, 27.8, 29.2, 29.9, 33.0, 35.6, 37.0, 40.5, 42.1, 43.2, 45.0.
There are 16 observations, so the lower half (first 8 values) is: 20.8, 22.3, 23.9, 24.4, 25.9, 26.6, 27.8, 29.2.
The first quartile is defined as the median of this lower half. For eight numbers, the median is the average of the 4th and 5th values in that half, which are 24.4 and 25.9.
Compute the average: (24.4 + 25.9) / 2 = 50.3 / 2 = 25.15.
Therefore, the Q1 value, expressed in thousands of dollars, is 25.15.
Note: If a different quartile convention is used (some textbooks use a slightly different method to define quartiles for small samples), you might get a different number, but the standard method applied here yields 25.15. The value 24.15 does not match this calculation and would reflect a different (nonstandard) convention or a data entry error.
In context of this dataset, the computed first quartile is 25.15 (in thousands of dollars).

The following are responses to a graduate survey on the salaries offered to Bachelor of Business graduates (in $ thous).45.0 42.1 29.9 22.3 35.6 23.9 27.8 40.5 25.9 26.6 33.0 29.2 37.0 20.8 24.4 43.2The first quartile for this data set is _______ $thous. (2 dec pl)

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