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Find the mode of the data:

[tex]\[
\begin{array}{rr}
\text{Range} & \text{Frequency} \\
20-30 & 5 \\
30-40 & 3 \\
40-50 & 12 \\
50-60 & 2 \\
60-70 & 6 \\
70-80 & 2 \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To find the mode of the given grouped data, we need to determine the class interval that has the highest frequency. Here is a step-by-step process:

1. List the class intervals with their corresponding frequencies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 20-30 & 5 \\ \hline 30-40 & 3 \\ \hline 40-50 & 12 \\ \hline 50-60 & 2 \\ \hline 60-70 & 6 \\ \hline 70-80 & 2 \\ \hline \end{array} \][/tex]

2. Identify the class interval with the highest frequency:
- The frequencies are: 5, 3, 12, 2, 6, 2.
- The highest frequency is 12.

3. Determine the modal class:
- The class interval corresponding to the highest frequency (which is 12) is 40-50.

Thus, the mode of the given data is the interval (40, 50), and the frequency of this modal class is 12. Therefore, the mode of the data is:

[tex]\[ \text{Modal class} = [40-50] \][/tex]
[tex]\[ \text{Frequency of the modal class} = 12 \][/tex]
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