Question

4 - 4. sam collected data by measuring the pencils of her classmates. she recorded the length of the painted part of each pencil and its weight. her data is shown on the graph at right.
a. describe the association between weight and length of the pencil. remember to describe the form, direction, strength, and outliers.
b. make a conjecture (a guess) about why sams data had an outlier.
c. sam created a line of best fit: ( w = 1.4+0.25l ) where ( w ) is the weight of the pencil in grams and ( l ) is the length of the paint on the pencil in centimeters. what does the slope represent in this context?
d. sams teacher has a pencil with ( 11.5 ) cm of paint. predict the weight of his teachers pencil.
e. interpret the meaning of the ( y )-intercept in context.

Explanation:

a.

Step1: Check the form

The data points seem to follow a linear pattern.

Step2: Check the direction

As the length of the paint (x - axis) increases, the weight (y - axis) also increases. So, it is a positive association.

Step3: Check the strength

The points are somewhat close to a potential line of best - fit, so it is a moderate association.

Step4: Check for outliers

There is one point at \(x = 2,y = 4.5\) which is far from the general trend of the other points.

An outlier could be due to a special type of pencil (e.g., a pencil with a different core material, a pencil with an eraser that is much heavier than the others, or a mis - measurement).

In the equation \(w = 1.4+0.25l\), the slope \(m = 0.25\). In the context of weight (\(w\)) and length of paint (\(l\)), the slope represents the change in weight for a unit change in the length of the paint.

Answer:

The association is linear, positive, moderate, and has one outlier.

b.