The following are thirteen 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 26.7 25.1 32.7 29.2 38.4The first quartile for this data set is _______ $thous. (2 dec pl)

Question

BlackTom AI · Accepted Answer

We start by restating the data and the task to find the first quartile (Q1) of the given salary data.
Data (13 observations, in thousands): 45.0, 42.1, 29.9, 22.3, 35.6, 23.9, 27.8, 40.5, 26.7, 25.1, 32.7, 29.2, 38.4.
First step: sort the data from smallest to largest to identify positions clearly. Sorted order is: 22.3, 23.9, 25.1, 26.7, 27.8, 29.2, 29.9, 32.7, 35.6, 38.4, 40.5, 42.1, 45.0.
With 13 data points, the median (the second quartile, Q2) is the 7th value, which is 29.9. This splits the data into a lower half and an upper half.
Second step: determine which data belong to the lower half for Q1. Using the common method for odd n (n = 13), the lower half consists of the first 6 observations: 22.3, 23.9, 25.1, 26.7, 27.8, 29.2.
Third step: find the median of the lower half to obtain Q1. Since there are 6 values in the lower half, Q1 is the average of the 3rd and 4th values in this subset: 25.1 and 26.7.
Compute: (25.1 + 26.7) / 2 = 51.8 / 2 = 25.9.
Alternative common method (inclusive/exact 0.25 position): some definitions use the formula Qp = value at position p*(n+1) with interpolation. Here p = 0.25 and n = 13 gives position 3.5, which lies between the 3rd (25.1) and 4th (26.7) values in the sorted data, and the interpolated value is 25.1 + 0.5*(26.7 - 25.1) = 25.9 again, confirming 25.9 as the Q1 under typical methods.
Note about the provided answer: if the stated answer is 25.10, this does not align with the standard quartile calculations shown above. The discrepancy suggests either a different convention for defining Q1 or a calculation/rounding inconsistency. The steps above illustrate the standard approach and yield 25.9 (in two decimals, 25.90).
In summary, after sorting and applying the conventional method to obtain Q1, the result is 25.9 (or 25.90 when expressed with two decimals). If your source lists 25.10, consider checking which quartile convention is being used and whether any data entry or rounding differences occurred.

The following are thirteen 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 26.7 25.1 32.7 29.2 38.4The first quartile for this data set is _______ $thous. (2 dec pl)

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