A quartermaster is recording the number of uniform items issued per day over an 8-day peri… — Armed Services Vocational Aptitude Battery (ASVAB)

A quartermaster is recording the number of uniform items issued per day over an $8$ -day period. The recorded numbers are $24$ , $19$ , $28$ , $17$ , $33$ , $16$ , $20$ , and $27$ . What is the median number of uniform items issued?

22Answer
B
23
C
25
D
44

Answer

The median number of uniform items issued is 22.

The correct answer accurately sorts the dataset into numerical order (

16, 17, 19, 20, 24, 27, 28, 33

) and calculates the average of the two middlemost numbers,

20

and

24

, which results in

22

Step-by-Step Solution

Sort the recorded numbers in ascending numerical order.

The sorted list is:

16, 17, 19, 20, 24, 27, 28, 33

The median is the middle value of an ordered dataset, so ordering is always the first step.

Identify the middle value(s).

Since there are

8

data points (an even number), there are two middle values: the 4th and 5th numbers, which are

20

and

24

An even number of data points does not have a single exact middle number.

Calculate the average (mean) of the two middle values.

\frac{20 + 24}{2} = \frac{44}{2} = 22

The median for an even number of data points is found by taking the mean of the two middlemost values.

Key Concept

To find the median of a dataset with an even number of values, the data must first be ordered from least to greatest, and then the mean of the two central values must be calculated.

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