The data given as a whole would be called ungrouped data. Now to get the variance, you will need the formula:
s^2= <u>Σ(x-mean)^2</u>
n
x = raw data
mean = average of all data
n = no. of observations
s^2 = variance
Now we do not have the mean yet, so you have to solve for it. All you need to do is add up all the data and divide it by the number of observations.
Data: <span>90, 75, 72, 88, 85 n= 5
</span>Mean=<u>Σx</u>
n
Mean = <u>90+75+72+88+85 </u> = <u>410</u> = 82
5 5
The mean is 82. Now we can make a table using this.
The firs column will be your raw data or x, the second column will be your mean and the third will be the difference between the raw data and the mean and the fourth column will be the difference raised to two.
90-82 = 8
8^2 =64
75-82 = -7
-7^2 =49
72-82 = -10
-10^2=100
88-82=6
6^2 = 12
85-82=3
3^2=9
Now you have your results, you can now tabulate the data:
x mean x-mean (x-mean)^2
90 82 8 64
75 82 -7 49
72 82 -10 100
88 82 6 36
85 82 3 9
Now that you have a table, you will need the sum of (x-mean)^2 because the sigma sign Σ in statistics, means "the sum of."
64+49+100+36+9 = 258
This will be the answer to your question. The value of the numerator of the calculation will be 258.
<u>
</u>
1.41/100 = 0.0141 * 15 = 0.21
$0.21
There are many different types of equations we can use to allow x to equal 19! Below are some examples :) See if you can come up with some on your own based off of these examples:
5x = 95.....................................Divide both sides b 5
x = 19.......................................There's one for you :)
_____________________________________________________________
1 + x - 5 = 15............................Combine like terms
x - 4 = 15..................................Add 4 to both sides
x = 19
_____________________________________________________________
There's just a couple of examples, but see if you can come up with some on your own and let me know if you get stuck!
Thank you for your question! I hope this helped! Have an amazing day and feel free to let me know if I can help you any further! :D
