Answer: Calculate the mean of a frequency table with intervals by using the midpoint of each interval multiplied by its corresponding frequency, and then dividing the sum by the total frequency.

Explanation:

Finding the mean of a frequency table with intervals involves calculating the weighted average of the values within each interval. Here’s a detailed explanation of the process:

1. Frequency Table with Intervals:
   • In a frequency table with intervals, data is grouped into intervals or ranges, and the frequency represents the number of observations falling within each interval.
2. The midpoint of Intervals:
   • The midpoint of each interval is the value that lies halfway between the lower and upper bounds of the interval.
   • To find the midpoint of an interval, simply add the lower and upper bounds and divide by 2.
3. Weighted Average Calculation:
   • To calculate the mean (average) of the frequency table with intervals, you need to compute the weighted average of the midpoints of the intervals.
   • Multiply each midpoint by its corresponding frequency to get the weighted value for that interval.
4. Example:
   • Suppose you have the following frequency table with intervals:
     [Tex][ \begin{array}{|c|c|} \hline \text{Interval} & \text{Frequency} \\ \hline 10 – 20 & 5 \\ 20 – 30 & 8 \\ 30 – 40 & 12 \\ \hline \end{array} ] [/Tex]
   • The midpoints of these intervals would be:
     [Tex]Midpoint of (10-20): ( \frac{10 + 20}{2} = 15 )\\ Midpoint of (20-30): ( \frac{20 + 30}{2} = 25 )\\ Midpoint of (30-40): ( \frac{30 + 40}{2} = 35 ) [/Tex]
5. Total Frequency:
   • Calculate the total frequency by summing up all the frequencies in the frequency table.
6. Mean Calculation:
   • Finally, divide the sum of the weighted values by the total frequency to find the mean: [Tex][ \text{Mean} = \frac{\text{Total frequency}}{\text{Sum of weighted values}} ] [/Tex]
7. Interpretation:
   • The mean of the frequency table represents the average value of the data, taking into account the frequency of each interval. It provides a measure of central tendency for the grouped data.