What is the value of the mode for this variable? What is the value of the median for this variable? What is the value of the minimum for this variable? What is the value of the 25th percentile for this variable?

Explanation:

The values are not reported, but I can use a hypothetical example to explain the concepts and illustrate their application.

Example: Find the mode, median, minimum value, and the value of the 25th percentile for the a variable with the following values: 10, 12, 14, 24, 32, 64, 66, 25, 30, 34, 40, 62, 66, 34.

General concept: mode, median, minimum value, 25th percentile, along with others, are statistics used to order and summarize data, to facilitate statistical inference.

To calculate mode, median, minimum and 25th percentile, you must first order the list. Thus:

Mode:

Mode is the value that repeats the most. A set of data may contain more than one mode.  This is precisely the case: 34 and 66 appear twice each.

Thus the modes are: 34 and 66.

Median:

Median is the value in the middle; the value that splits the list in two parts with the equal number of data. When the number of data is odd it is the mid value; when the number of data is even, it is the average of the two values in the middle.

This list has 14 numbers, thus the median is the average of the two middle values: the seventh and the eigth value.

It is easy to see it if you split the list in this way:

Then, the median is (32 + 34) / 2 = 33

Minimum:

It is the lowest value in the set of data. Thus it is 10.

25th percentil

25th percentil is the value below which 25% of the data lie.

It is the same that first quartile.

It is also the median of the first half of data: because it is the half of the half.

Thus, use the first 7 data:

The median of those data is 24. Thus the 25th percentile is 24: 24 splits the first 25% of the data from the rest.

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