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Bowden Russell

Welcome to my online classroom. 

7th Grade Math Work for April 6th to April 12th:

Introduction to Statistics We went over our introduction to statistics in our last week and took notes on:

  1. The Mean.  Add up all the values of the data points then divide by the number of data points. Mean also is the same as “average”.  
  2. The median. The number in the middle.  Arrange the data points from smallest to largest then locate the number in the middle.  If there are an even number of data points you find the average of the two points in the middle
  3. The Mode.  The number that occurs most often.  There can be more than one mode on occasion.
  4. MAD: Mean average deviation. This concept is used to determine how spread out the set of data points is. You find the MAD by first finding the Mean (see “a” above) then subtract each data point from the value of the Mean , taking the absolute value of that subtraction (you’ll always have a positive number).  Then add up all those absolute values….then divide by the number of data points.  We did an example of this on the last day of class before break.

 

 

Here is a video from Khan Academy for an Introductory to Statistics:

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/measuring-center-quantitative/v/statistics-intro-mean-median-and-mode

 

Pay attention to the vocabulary in the video.  

 

Problem of the week: 

 

Find the Mean, Median and Mode as well as the MAD of the following data set (you can use a calculator)

6, 7, 12, 6, 11, 15, 20, 22, 8, 6, 11, 8, 14 20, 22 40.

 

Write down all your work on paper, take a picture of your work then send it to me via email!  

 

Good luck!!!


April 16th to April 23rd.

 

Answers to last week’s problem:  Adding all the numbers up you get 228.  Then divide this number by the number of data points, which is 16, you get 14.25.  The mean is 14.25.

 

The MEDIAN:: Arranging the numbers from smallest to greatest :

6,,6 ,7, 8, 8, 11, 11, 12, 14, 15, 20, 22, 22, 40.

Now cancel the outer numbers till you get to 11 and 12.  The average of these two numbers is 11.5.  That is the MEDIAN.

 

The mode is the most frequent data point.  6, 11, 8 and 22 all appear twice.  Thus, we have those 4 points as the MODE.  Yes, you can have more than one number be the mode.

 

Now, we find the MAD, “Mean Average Diviation”.  We take each data point, there are 16 of them, and subtract them from the mean, which we found wa 14.25 from our first calculation.  We then take the absolute value, so we’ll always have a positive number, the add them up.  Then we divide by the number of data points, which is 16.

 

So the sum (addition) of these 16 subtractions is 89.55.  Now dividing this by the number of points, 16, gives us a MAD of 5.596875. Pretty cool, eh?  The MAD gives you an idea of how widely dispersed (spread out) the data set is.  

Okay, on to new stuff….

SQUARE ROOTS AND CUBE ROOTS!

What is a “square root”?  It is asking you, “what number time itself gives you this number?”

For example, what is the “Square Root of 25”?  Okay, what number times itself is 25? That’s easy, you should already know that 5 times 5 is 25, so the square root of 25 is 5!

Cube roots? Again, it is much like “Square Roots”, but this time it is asking you,”What number times itself THREE TIMES, gives you this number”?

For example: What is the cube root of 64?  Four!  4 times 4 times 4 = 64, so the cube root of 64 must be 4!  

You should be able to do these in your head and that means you know your multiplication tables.  I also want you to know your multiplication tables up to 30.  Yes, beyond 12 times 12.  I want you to know them all up to 30.  This is a goal mind you, not something I expect you to know by next week.  If you don’t know your multiplication tables up to 12 then learn them.  they aren’t hard.  The week after you should know up to 20 times 20.  Two weeks later up to 25 times 25.  The week after you should know up to 30 times 30.   Yes,  it is an obtainable goal and you will learn them.  

Here is a video you can watch to help you and give you practice.

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/e/cube_roots

Homework:

Find the square root of the following numbers:

  1. 36
  2. 49
  3. 121
  4. 64
  5. 144
  6. 100

Find the cube root of the following numbers:

‚Äč       7. 27

  1. 64
  2. 1000
  3. 125
  4. 729
  5. 512

Good luck. Email me the answers.


April 27th to April 30th, 2020.

Last week we discussed square and cubic roots.  You’ll be starting out with them in August.  Let’s expound on that, shall we?

As we saw last week finding the square root of a perfect square is easy.  What is the square root of 25? Well, 5 x 5 is 25 so the square root is 5!  But life is rarely that easy, right? What if you were asked to find the square root of 26?  Guess what? There is no perfect square root of 26.  It is what we call an “Irrational number”.  If you take the square root of 26 on your calculator you get….5.099019514, but the reality is your calculator stopped at the 4 when it could have gone on forever if it had a large enough screen!!!

So lets see how we, without a calculator can approximate the square root of a non-perfect square  Take the SQR(37)-that is how you write “find the square root of 37”.  So find what two perfect squares 37 lies between: 36 and 49.  We know the SQR36 is 6 and the SQR49 is 7, so SQR37 must lie between 6 and 7! So it will be “6 point something”.  Hmmmmm.  Well 37 is much closer to 36 than it is to 49 so I’ll guess 6.1.  On the calculator it says,”6.08”.  Pretty good! I was off by only .02!

Let’s try another one: SQR79.  Well 79 lies between 64 and 81.  The SQR64 is 8 and the SQR81 is 9, so the SQR79 must be between 8 and 9.  So “8 point what?”.  Hmmmm. Well 79 is 15 away from 64 and only 2 away from 81, so the SQR79 must be about 8.8 I guess.  The Calculator says: 8.88!  Not bad, I was only off by .08!  

So try the following and send me an email letting me know how close you go to the calculator answer:

Find the SQR of:

1. 99

2. 48

3. 55

4. 30

5. 140

 

Have a great week and keep in touch!

 

 

Bowden Russell

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