June 13

Math 9 Misleading Statistics by Brandon and Rylee

Influence of collected data

Bias: Already being in favour of one side, Ex: Most people agree that smoking is bad for you and could kill you, do you agree?

Use of Language: Wording a sentence in an easy to understand way. Ex: Are sweatshops good or bad?

Ethics: Are you trying to show the truth? Ex: If there was a poll for the best shoe companies and you can check more than one, but the companies says that 80% of people check yours so you say that but, they also check other things.

Cost: Does it cost more to make the survey than what you get back?

Time and timing:  The information is collected at an inappropriate time that would impact the people’s choice. Ex: If you asked Fort McMurray residents if the government should increase fire support.

Privacy: Is the graph kept confidential, do the people have a right to refuse answering the question

Cultural sensitivity: Maybe the graph had a question that offended people from different cultures

Explain the difference between a population and a sample:

Population:   A population is a group of objects that have things in common which is relevant to the data being collected. The point of a statistical population is to collect information about a chosen population

Sample:  A sample is a set of objects chosen from a complete sample in a random order example: choosing every 10th person who walks through the door. The point of a sample is to collect data that is unbiased.

Explain the different types of sampling methods and the benefits of each

Convenience sample:  Made up of people who are easy to reach or contact. Benefit is that the survey will probably be finished quickly. Ex: a survey interviews shoppers at a local mall. If the mall was close to the surveyors business this would be considered a convenience sample.

Random:  Chosen in a random order or way. Names in a hat then the person is blindfolded and picks a name. A good thing is that the data will be random and not biased.

Voluntary response: This type of response can easily become bias because the sample members are self-selected for example on the radio when you hear people call in to talk about things like gun control, of course they will chose to be against it because that was what the show was talking about.

Stratified sample: The population is separated into groups based on similar things, then ask a few people from that group. (Ex: male and females, children and adults, similar interests)

Systematic sample: This is where you divide the population size by the desired sample size. This can be bias because they can choose only people who agree with the company. For example: A shoe company starts a poll to see who their favourite shoe company is but, they only ask from the people who frequent their store.

). Give examples. Explain how choosing an inappropriate sampling method may bias the data. Give Examples

Explain the difference between theoretical and experimental probability.

Theoretical Probability:  The number of ways a situation could play out, divided by the total number of outcomes. Basically it’s what are the odds of an event happening. What is expected to happen based on the outcomes. Example: a shoebox has 10 red shoelaces, 8 blue shoelaces, and 2 yellow shoelaces. What is the theoretical probability of picking a blue shoelace?

Experimental Probability:  The ratio of the amount of times a situation occurs to the total number of times the event is performed. The result of a situation after a number of trials. Example: a box contains 10 pink stuffed animals, 8 purple stuffed animals, and 2 blue stuffed animals. What is the experimental probability of picking a blue marble?

Find 3 examples (different from the examples already discussed in class) of misleading statistics used in the media and explain why they are misleading

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This statistic was obviously made by someone who is either selling houses or works in the industry because they are trying to show that the prices barely moved in scale but in reality prices went up 10 000

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This statistic makes it seem like Clinton was way worse than Bush for unemployment but if you look at the numbers they are barely different they did not start the numbers at 0.

mjb

This statistic is misleading because they started the graph at 7% if it started at 0 it would look like a lot less, they zoomed in on the top.

Category: Grade 9, Math 9 | LEAVE A COMMENT
November 23

Everything I know about Exponents (Redone)

 Brandon Henricksen   Block B, Ms. Hubbard

 

  • Represent repeated multiplication with exponents

We use exponents to write out equations faster and easier

Eg: 105= 10 x 10 x 10 x 10 x 10 = 100 000

Describe how powers represent repeated multiplication

 

The power are the numbers that are being multiplied

Eg: 105= base x base x base x base x base= product

  • Demonstrate the difference between the exponent and the base by building models of a given power, such as 23 and 32.

 

In the equation= 2^3, the 3 represents that it’s a cube, and the 2 is the length, height, and width of the cube and therefore also equals how many squares on in each face if you see it that way.

         . Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as 23 and 32.

2^3is 2 x 2 x 2 its 2 multiplied by itself 3 times. While 3^2 is 3 x 3, 3 multiplied by itself 2 times

        . Evaluate powers with integral bases (excluding base 0) and whole number exponents.

(-5)^2 would be 25 because if the exponent is an even number the answer is positive

  • Explain the role of parentheses in powers by evaluating a given set of powers such as (-2)4, (-24) and -24.

The parentheses are to tell you what the answer is going to be for example if you have -2^4 when you turn it into a extended answer it is -1 x 2 x 2 x 2 x 2 as for (-2^4) would be 16 because it is even but (-2)^4 is -16 because it is multiplying

  • Explain the exponent laws for multiplying powers with the same base.

When you are multiplying, and the bases are the same, you add the exponents

Ex:

 

         . Explain the exponent laws for dividing powers with the same base

When you are dividing and the bases are the same subtract the exponents

Ex: x^5 / x^2 = x^3

  • Explain the exponent laws for raising a product and a quotient to an exponent.

(2a)4  =  (2a)(2a)(2a)(2a)  =  (2 • 2 • 2 • 2)(a • a • a • a) = (24)(a4) = 16a4

        You multiply both 2 and a

Voilà…

 

Explain the law of powers with an exponent zero

 

Any number except zero raised to an exponent of zero equals 1

Ex: 50= 1, 10002130194321743^0 = 1

Use patterns to show that a power with an exponent of zero is equal to one.

When you have a negative exponent, it is equal to 1/ the base to the positive exponent, so in your case, 17^(-5) = 1/(17^5). Plus, we know that when we multiply to exponents of the same base together, the new exponent is the sum of the two exponents on the left. So 17^4 * 17^9 = 17^(9+4) = 17^13 If we had 17^5 * 17^(-5), we get two results:  we get that this = 1 because any number divided by itself is 1.
we get that this = 17^0 because 5-5 = 0.
So we combine these two and find that 17^0 = 1.

  • I can apply the laws of exponents

 

Exponents is however many times the base number must be multiplied by itself

Ex: 10^4 = 10 x 10 x 10 x 10

  • I can identify the error in a simplification of an expression involving powers

 

INCORRECT = 5^2 x 5^3 = 5^2×3 = X

CORRECT= 5 ^2 x 5^3 = 5^2+3 = 5^5 = 3,125

  • Use the order of operations on expressions with powers

2 + 6 (3 + 1)^2

2 + 6 (4)^2

2 + 6 (16)

2 + 96

= 98

 

Brackets first, so you’d figure out 3 squared, and then you’d multiply that by itself four times.

  • Determine the sum and difference of two power

The sum of any two terms multiplied by the difference of the same two terms is easy to find and even easier to work out — the result is simply the square of the two terms. The middle term just disappears because a term and its opposite are always in the middle.

  • If you encounter the same two terms and just the sign between them changes, rest assured that the result is the square of those two terms. The second term will always be negative, as in the example,
  • Example: (x– 4)(x + 4)

 

  • Identify the error in applying the order of operations in an incorrect solution

 

INCORRECT= 5 x (2^2) + 3 x 2 = 46 The person did not use BEMDAS correctly

CORRECT= 5 x (2^2) + 3 x 2 =

  • Use powers to solve problems (measurement problems)

If a lego has a total area of 100cm^2 what are the measurements?         

25cm + 25cm + 25cm + 25cm = 100cm^2 or 25^2 + 25^2 = 100cm^2 

  • Use powers to solve problems (growth problems)

 

If the amount of people currently online are 10 but they double every hour how many will we have in

3 hours:                                         6 hours:                                     10 hours:

20 x 3 = 60                              240 x 2 = 480                              3840 x 2 = 7 680

60 at 3 hours                                 480 at 6 hours                        7 680 at 10 hours                                

Category: Math 9 | LEAVE A COMMENT