Misleading Statistics
The majority of statistics are reputable, and can be trustworthy. True or False?
False, 67% of statistics are made up!
What do the variables "m" and "b" represent in a linear equation?
m = slope
b = y-intercept
What would be the line of best fit for the following values:
x: 1 2 3 4 5 6
y: 77 65 69 52 48 72
y = -2.66x + 73.13
What is the format for an exponential equation?
y = a(b)x
What is the difference between joint frequencies and marginal frequencies?
Joint - middle data points (anything that isn't a total)
Marginal - Totals
How can you prevent reporting misleading statistics?
Find the slope using these 2 data points:
(0,5) (3,20)
m = (20 - 5)/(3 - 0) = 5
What does it mean for a scatterplot to have a correlation close to 1?
The line of best fit is really good.
In this equation, what is the y-intercept?
y = 5(10)x
5.
How do you get the frequencies of a two-way table? (Think about the first step in a two-way table problem, what is the first thing you have to do to the table?)
Divide everything by the total. Usually this number is 100, in which case you can just convert everything to a decimal, but when its not 100, for example 250, you would have to divide everything by 250.
What is wrong with this graph? (NASA Image)
Only has a snip bit of the time frame, does not include all of the information.
The slope of an equation is -2/3. The line of best fit passes through the point (6,7). Write the equations in linear form.
y=-2/3x + b
7 = -2/3(6) + b
7 = -4 + b
11 = b
y = -2/3x + 11
How can you tell if a scatterplot will be linear or exponential?
There are many answers: Plotting the points and looking at it, seeing if the value converge, by looking at a table you can do the differences v. ratios and see if its exponential or linear, etc.
When looking at table, you can determine whether the graph will be exponential or linear. This can be known by computing the differences and ratios of the values. Is an exponential equation going to have the same number for differences or for ratios?
Ratios.
What is the joint frequency of children ages 6 - 10 who prefer vanilla?
29%
How can you tell when a statistic is misleading?
Look at the x and y axis and make sure they are not only in order, but that information is not missing from them. Make sure the information presented isn't from a non-credible source. Make sure all information is given, not just pieces.
x values: 1,2,3,4,5,6
y-values: 3,6,9,12,15,18
Write the equation of the line.
Whatever's in your calculator is probably right.
True or false: I can figure out a future data point on a scatterplot with a correlation of close to 0 by plugging in either an x or y value, then computing.
False, the correlation is close to 0 which means there is no line of best fit.
Find the equation for this table.
x: 1 2 3 4 5 6
y: 36 72 144 288 576 1152
y = 18(2)x
What is the conditional relative frequency of kids who prefer chocolate ice cream, given they are ages 10-13?
0.24/0.54 = 44%
Toby stands outside a Target and surveys people walking around. Toby asks them whether they prefer shopping at Target or Walmart. Toby published the statistic: "92% of shoppers prefer Target over Walmart for their shopping needs."
Why is this statistic misleading?
Toby is standing outside a Target...
4x = 2y + 8
2y = 4x - 8
y = 2x - 4
Draw it.
What is the correlation for this table?
x: 1 2 3 4 5 6
y: 4 9 5 2 3 7
r = -0.12 (or close to 0). Bad correlation, very bad.
I couldn't figure out another question for exponential equations, so if you can answer this random question I'll give you the points: How many degrees does Ms. Borges have?
4, going on my 5th.
jrf of ages 6 - 10 who prefer chocolate/mrf of ages 6-10 = 0.14/0.46 = 30%
mrf of who prefers chocolate/total # = 0.38/1 = 38%
There is a difference, so there is an association between the two.