how to find the mean of the frequency distribution
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The formula to notice the mean of grouped data from a frequency tabular array is given below. Scroll down the folio for more examples and solutions.
How To Find The Hateful From A Frequency Distribution Tabular array?
The following case shows how to decide 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 | twoscore – 44 | 45 – 49 | fifty – 54 | 55 – 60 |
|---|---|---|---|---|---|
| Frequency | half dozen | 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 | xl – 44 | 45 – 49 | 50 – 54 | 55 – 60 |
|---|---|---|---|---|---|
| Frequency (f) | 6 | 12 | 15 | 10 | seven |
| Mid-betoken (x) | 37 | 42 | 47 | 52 | 57 |
Step 2: Multiply the frequency of each interval past its mid-signal.
| Bore (mm) | 35 – 39 | 40 – 44 | 45 – 49 | 50 – 54 | 55 – 60 |
|---|---|---|---|---|---|
| Frequency (f) | 6 | 12 | fifteen | x | 7 |
| Mid-signal (x) | 37 | 42 | 47 | 52 | 57 |
| f × 10 | 222 | 504 | 705 | 520 | 399 |
Step 3: Go the sum of all the frequencies (f) and the sum of all the fx. Divide 'sum of fx' by 'sum of f ' to go the mean.
| Total | ||||||
|---|---|---|---|---|---|---|
| Diameter (mm) | 35 – 39 | forty – 44 | 45 – 49 | 50 – 54 | 55 – 60 | |
| Frequency (f) | 6 | 12 | fifteen | 10 | 7 | fifty |
| Mid-indicate (x) | 37 | 42 | 47 | 52 | 57 | |
| f × ten | 222 | 504 | 705 | 520 | 399 | 2350 |
How To Observe The Mean, Mode And Median From A Frequency Table For Both Discrete And Grouped Information?
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 to a higher place half the total contains the median.
- Prove Video Lesson
How To Observe The Mean From A Frequency Table For Discrete Information And Continuous (Grouped) Data?
- Prove Video Lesson
How To Get Averages From Grouped Frequency Tables, Including The Range, Hateful, Median And Mode?
- Prove Video Lesson
How To Work Out The Hateful From A Grouped Frequency Tabular array?
First work out the midpoints of each group. And so multiply the midpoints by the frequency. Divide the total of this cavalcade by the total frequency.
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How to utilise 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 past the following frequency distribution.
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How to employ a TI-84 calculator to calculate the Mean and Standard Divergence of a Grouped Frequency Distribution?
Find the hateful and the standard departure of the sample data summarized by the following frequency distribution.
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