# Discover How To Find the Mean From Frequency Tables With Intervals (Step-by-Step Video Lessons, Examples & Solutions)

Introduction:

Are you struggling with finding the mean of grouped data from a frequency table? Well, worry no more! In this article, we will take you through step-by-step instructions on how to find the mean, mode, and median from a frequency table, how to work out the mean from a grouped frequency table, and how to use a TI-84 calculator to calculate the mean and standard deviation of a grouped frequency distribution.

Example:

- Suppose you have a frequency distribution table for the diameters of 40 bottles, measured in millimeters. To find the mean, follow these simple steps:
- Step 1: Finding the midpoint of each interval

To find the midpoint of an interval, add the lower class limit to the upper class limit and divide by 2. For instance, the midpoint of the interval 35 – 39 is (35 + 39) ÷ 2, which equals 37.

Step 2: Multiplying the frequency of each interval by its midpoint

After finding the midpoint of each interval, multiply it by the frequency of the interval. For example, for the interval 35 – 39, multiply 37 by 6 to get 222.

Step 3: Summing the frequencies and the fx column

After step 2, add up all the frequencies and the fx column. In this case, the sum of the frequencies is 50, and the sum of the fx column is 2350.

Step 4: Dividing the sum of fx by the sum of frequencies

Finally, divide the sum of fx by the sum of frequencies to get the mean. In this case, the mean is 2350 ÷ 50, which equals 47 millimeters.

How to Find Mean, Mode, and Median from Frequency Tables:

Apart from finding the mean, you can also calculate the mode and median for discrete and grouped data from a frequency table. To calculate the mode, find the largest frequency, and the corresponding value is the modal value or modal class. On the other hand, to calculate the median, calculate a running total of the frequencies, and the first interval that is above half the total contains the median.

How to Work Out the Mean from a Grouped Frequency Table:

To work out the mean from a grouped frequency table, first find the midpoints of each group. Afterward, multiply each midpoint by its corresponding frequency, then sum up all the products. Finally, divide the total of this column by the total frequency of all intervals.

How to Use a TI-84 Calculator to Calculate the Mean and Standard Deviation of a Grouped Frequency Distribution:

Calculating the mean and standard deviation for a grouped frequency distribution can be challenging, but with a TI-84 calculator, it becomes a breeze. We have attached a video lesson that explains, step-by-step, how to use a TI-84 calculator to calculate the mean and standard deviation of a sample data summarized by a grouped frequency distribution. The video will be instrumental in understanding how to harness the power of a TI-84 calculator.

Mathway Calculator and Problem Solver:

Mathway is a free calculator and problem solver for various math topics. The calculator handles various mathematical problems, including statistical operations like finding the mean and standard deviation. Type in your problem, and the calculator will show you step-by-step instructions on how to solve the problem. Mathway provides an excellent tool for students to practice the various mathematical concepts taught in class.

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