What is the formula for the arithmetic mean as calculated from a frequency distribution?

How to find the Mean of Grouped Data?

The formula to find the mean of grouped data from a frequency table is given below. Scroll down the page for more examples and solutions.

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How do you find the arithmetic mean of a frequency distribution?
What is the formula for calculating arithmetic mean?
What is the formula for arithmetic mean of grouped data?
How do you find the arithmetic mean from the following data?

How To Find The Mean From A Frequency Distribution Table?

The following example shows how to determine the mean from a frequency table with intervals or grouped frequency table.

Example:
The following table shows the frequency distribution of the diameters of 40 bottles. (Lengths have been measured to the nearest millimeter) Find the mean of the data.

Diameter (mm)	35 – 39	40 – 44	45 – 49	50 – 54	55 – 60
Frequency	6	12	15	10	7

Solution:
Step 1: Find the midpoint of each interval.

Midpoint of interval =

(Lower class limit + Upper class limit)
=

(39 + 35) = 37

Diameter (mm)	35 – 39	40 – 44	45 – 49	50 – 54	55 – 60
Frequency (f)	6	12	15	10	7
Mid-point (x)	37	42	47	52	57

Step 2: Multiply the frequency of each interval by its mid-point.

Diameter (mm)	35 – 39	40 – 44	45 – 49	50 – 54	55 – 60
Frequency (f)	6	12	15	10	7
Mid-point (x)	37	42	47	52	57
f × x	222	504	705	520	399

Step 3: Get the sum of all the frequencies (f) and the sum of all the fx. Divide ‘sum of fx’ by ‘sum of f ’ to get the mean.

						Total
Diameter (mm)	35 – 39	40 – 44	45 – 49	50 – 54	55 – 60
Frequency (f)	6	12	15	10	7	50
Mid-point (x)	37	42	47	52	57
f × x	222	504	705	520	399	2350

How To Find The Mean, Mode And Median From A Frequency Table For Both Discrete And Grouped Data?

Mean: multiply midpoints by frequencies and add the sub-totals. Divide by the total of the frequencies.

Mode: find the largest frequency - the corresponding value is the modal value or modal class.

Median: calculate a running total of the frequencies - the first interval that is above half the total contains the median.

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How To Find The Mean From A Frequency Table For Discrete Data And Continuous (Grouped) Data?

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How To Get Averages From Grouped Frequency Tables, Including The Range, Mean, Median And Mode?

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How To Work Out The Mean From A Grouped Frequency Table?

First work out the midpoints of each group. Then multiply the midpoints by the frequency. Divide the total of this column by the total frequency.

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How to use a TI-84 calculator to calculate the Mean and Standard Deviation of a Frequency Distribution?

Find the mean and the standard deviation of the population data summarized by the following frequency distribution.

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How to use a TI-84 calculator to calculate the Mean and Standard Deviation of a Grouped Frequency Distribution?

Find the mean and the standard deviation of the sample data summarized by the following frequency distribution.

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How do you find the arithmetic mean of a frequency distribution?

We then find the sum of all the frequencies and the multiplication of frequency of each class with the mid-point of that class. We then use formula of the mean of the grouped frequency distribution is given as ¯x=∑fixi∑fi to find the mean of the frequency distribution.

What is the formula for calculating arithmetic mean?

One method is to calculate the arithmetic mean. To do this, add up all the values and divide the sum by the number of values. For example, if there are a set of “n” numbers, add the numbers together for example: a + b + c + d and so on. Then divide the sum by “n”.

What is the formula for arithmetic mean of grouped data?

The formula used for arithmetic mean of grouped data by shortcut method is xˉ=A+∑f∑fd. A= Assumed mean of the given data. ∑f= Summation of the frequencies given in the grouped data. ∑fd= Summation of the frequencies and deviation of a given mean data. d= deviation of a mean data.

How do you find the arithmetic mean from the following data?

There are two steps to find the arithmetic mean in statistics: sum up all the numbers given in a set and then divide it by the total number of items in your set. The arithmetic mean is found similarly to a sample mean.