The test scores of a geometry class are given below. 90, 75, 72, 88, 85 The teacher wants to find the variance for the class pop
2 answers:
<h2>Answer:</h2>
The value of the numerator of the calculation of the variance= 258
and Variance= 51.6
<h2>Step-by-step explanation:</h2>We know that in order to calculate the variance we need to follow following steps:
- First calculate mean.
- Then subtract each of the data points from means and square the difference quantity.
- Lastly calculate the mean of these squared quantity.
The data points are:
90, 75, 72, 88, 85
The mean of these data points are:
Now on finding the difference terms i.e.
90-82=8
75-82= -7
72-82= -10
88-82=6
and 85-82=3
The square of these difference term is:
8²=64
(-7)²=49
(-10)²=100
6²=36
and 3²=9
Hence, the mean of these squared quantity i.e. Variance is:
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Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)