U6S Review Day 2

Which of the following correlation coefficients represents the best fit line for data?

(hint: think about absolute value)

• -0.43

• 0.74

• 0.03

• -0.81

• -0.61

Answer explanation

Step 1: look for closest value to -1 and 1

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Closest value to -1 → -0.81

Closest value to 1 → 0.74

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Step 2: look at absolute values (this means to turn any negative into a positive)

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-0.81 → 0.81

0.74 → 0.74

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Step 3: pick higher absolute value decimal

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Best coefficient here is -0.81 (this had a higher absolute value)

The data gathered and recorded in the scatter plot represents the grams of fiber, y, as a function of calories, x, present in quarter-cup servings of different green leafy vegetables.

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Which statement below is true?

• There is a strong correlation between x and y; here x causes y.

• There is no association in the data; here x does not cause y.

• There is an association between x and y; here we do not know why there is an association

• There is a strong negative linear correlation between x and y; here y causes x

Answer explanation

Step 1: association?

There is a strongly negative linear association

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Step 2: explanation?

The question does not explain at all why the variables are related, so we cannot say x controls y, or that y controls x

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Answer is: "there is an association, but we do not have an explanation for why"

What is the shape of the histogram?

(bonus: what math language keyword is used to determine the direction of skew)

• skewed left

• skewed right

• symmetrical

• uniform

Answer explanation

This histogram is skewed left, because fewer shaded regions exist on left

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Math language uses the word "outliers" to define the direction of skew

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Skewed left because "fewer shaded regions" exist on left

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Skewed left because "outliers" exist on left

What is the shape of the histogram?

(bonus: what math language keyword is used to determine the direction of skew)

• skewed left

• skewed right

• symmetrical

• uniform

Answer explanation

This histogram is symmetric

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Math language uses the word "outliers" to define the direction of skew

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Symmetric because "outliers" not present in data

Which box-and-whisker has a larger spread?

(bonus: what determines if data has small spread or large spread)

• Team A

• Team B

• Cannot determine

Answer explanation

Both teams are skewed right

"Longer whiskers" on the right

"Outliers" on the right

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IQR (box region) is the best measure of spread for skewed data

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Team A has a larger spread (because larger IQR in blue)

Team B has a smaller spread (because smaller IQR in yellow)

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In summary, Team A has more outliers than Team B, which is why Team A has a larger spread (the shaded region in blue) and longer whisker

Data was collected on the number of siblings for students in one classroom. The results are shown on the table.

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What is the min and max value for the data?

(find without using Desmos)

Answer explanation

Min = 0

Max = 4

Range = Max - Min = 4 - 0 = 4

Data was collected on the number of siblings for students in one classroom. The results are shown on the table.

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What is the median value for the data?

(find without using Desmos)

Answer explanation

The table means we have the following numbers:

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0, 0, 0, 0

1, 1, 1, 1, 1, 1, 1, 1

6, 6, 6, 6, 6, 6

3, 3, 3

4

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If you eliminate the smallest and largest numbers, then you can find the median

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First, four numbers were eliminated on both sides (shaded in red)

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Next, 6 numbers were eliminated on both sides (shaded in green)

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The remaining numbers are the median (shaded in black)

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Median = 1

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We know have an approximate guess of how the box-and-whisker plot looks without using Desmos

An executive at a car company wants to examine the relationship of cars sold, C, as a function of money the company spends on marketing, M. (data is represented as thousands on the x and y axis)

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How can we label the x and y axis?

Evaluate responses using AI:

OFF

Answer explanation

The phrase "as a function of" lets you know how to label the x and y axis

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In math it is understood that words before "as a function of" represent y, and those after represent x

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y = Car Sales (C)

x = Marketing Budget (M)

An executive at a car company wants to examine the relationship of cars sold, C, as a function of money the company spends on marketing, M. (data is represented as thousands on the x and y axis)

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What do we know about the line of best fit for the data without using Desmos? (think about variables for x and y, and value of y-intercept)

Evaluate responses using AI:

OFF

Answer explanation

y = mx + b

This is the equation for a line

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Look at the axis labels

y = Car Sales (C)

x = Marketing Budget (M)

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Instead of using y and x in the equation, we will use C and M

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C = mM + b

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m = slope = unknown

b = y-intercept = we can guess

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The y-intercept will be more than 20 but less than 30, so lets pretend it will be 25

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C = mM + 25

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