College

Use the frequency table to answer the following question:

\[
\begin{tabular}{|c|c|c|}
\hline
Grade & Interval & Frequency \\
\hline
A & 90-100 & 3 \\
B & 80-89 & 5 \\
C & 70-79 & 8 \\
D & 60-69 & 4 \\
F & 50-59 & 2 \\
\hline
\end{tabular}
\]

In what interval is the median located?

A. 80-89
B. 70-79
C. 60-69

Answer :

To find the interval in which the median is located, we need to first determine the total number of observations and then locate the median value based on that.

Here's a step-by-step explanation:

  1. Calculate the Total Number of Observations:

    • Add up all the frequencies from the table:
      [tex]3 + 5 + 8 + 4 + 2 = 22[/tex]
    • There are 22 observations in total.

  2. Find the Median Position:

    • The median is the middle value of a data set. For an even number of observations, such as 22, the median is the average of the 11th and 12th values when the data is ordered.

  3. Locate the Median Interval:

    • According to the frequency table:
      • The first 3 values fall in the [tex]90-100[/tex] range.
      • The next 5 values (4th to 8th) fall in the [tex]80-89[/tex] range.
      • The next 8 values (9th to 16th) fall in the [tex]70-79[/tex] range.
    • Since the 11th and 12th values fall within the [tex]70-79[/tex] range, the median is located in this interval.

Therefore, the median is located in the interval 70-79.

The correct answer is: B. 70-79.

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