Today I'll be talking about how to find the mean in grouped distributions. I'm sure most people would know how to search mean. You need to search the sum of the datas and divide it by the number of values like this:
Q) 3, 1, 5, 7, 13, 9, 12, 3, 18, 11, 2, 18, 12, 19, 20, 5, 8, 17, 14 and 16. These are the scores of a video game for 20 people. Find the mean from their scores.
First you add up the numbers: 3+1+5+7+13+9+12+3+18+11+2+18+12+19+20+5+8+17+14+16
=213
Then you divide it by the number of values: 213/20 = 10.65
So therefore the mean is 10.65.
Then you make a grouped frequency table:
Score
|
Frequency
|
1 - 4
|
4
|
5 - 8
|
4
|
9 - 12
|
4
|
13 - 16
|
3
|
17 - 20
|
5
|
So 4 people got scores between 1 and 4, another 4 got scores between 5 and 8, etc..
Now that you know how to find the mean you might ask what mean in grouped distributions mean.
In the procedure above you could know what are the scores of each person but what if the only information you received was the table. Could you still search for the mean? Not accurately but you can estimate and that's what you call finding mean in group distributions.
Firstly you'll have to find the midpoints of the score. To find the midpoint you'll have to add the two numbers and divide by two:
1+4 = 5 5/2 = 2.5
5+8 = 13 13/2 = 6.5
9+12 = 21 21/2 = 10.5
13+16 = 29 29/2 = 14.5
17+20 = 37 37/2 = 18.5
Then you'll have to multiply each midpoint with the frequencies:
2.5 x 4 = 10
6.5 x 4 = 26
10.5 x 4 = 42
14.5 x 3 = 43.5
18.5 x 5 = 92.5
and add them all together: 10+26+42+43.5+92.5 = 214
then divide by the number of people or the sum of the frequencies which is 20:
214/20 = 10.7
You can see that it's very close to the answer that we got earlier. So that's how you find the meaning grouped distributions. I hope this has helped you understanding means in grouped distributions a bit. I hope to see you guys again!
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