The data set is: 62, 75, 70, 68, 72, 78, 65, 70, 74, 69, 71, 73, 67, 70 Determine Q1.

Question

BlackTom AI · Accepted Answer

We need to determine Q1 (the first quartile) for the data set: 62, 75, 70, 68, 72, 78, 65, 70, 74, 69, 71, 73, 67, 70.

First, sort the data in ascending order to clearly see the distribution:
62, 65, 67, 68, 69, 70, 70, 70, 71, 72, 73, 74, 75, 78.

With 14 data points, a common way to find Q1 is to take the median of the lower half of the data (the first 7 values). The lower half is:
62, 65, 67, 68, 69, 70, 70.
The median of this lower half is the middle value (4th value) of these seven numbers, which is 68.

Now evaluate the answer choices:
- Option a: 68. This matches the computed Q1 using the lower-half-median method, so it could be correct under this convention.
- Option b: 67. This is the 3rd value in the sorted list and would be the median of a smaller subset, but not the lower-half median in the standard split for n = 14.
- Option c: 69. This is the 5th value in the lower half, not the median of the lower half, so it does not represent Q1 under the lower-half method.
- Option d: 70. This value appears in the data, but it is not the median of the lower half and thus not Q1 by this definition.

Consideration of the method matters: some textbooks define Q1 as the median of the lower half (as done here), while others interpolate between values. In this dataset, using the lower-half median yields 68, which aligns with option a. The other options correspond to single data points in the lower half or beyond, but do not represent the first quartile under this common convention.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

The data set is: 62, 75, 70, 68, 72, 78, 65, 70, 74, 69, 71, 73, 67, 70 Determine Q1.

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