Exploring Data

If all of the below sets have the same mean. Which set of the data probably has the points closest to the mean?

Set 1-Standard Deviation=3.1

Set 2-Standard Deviation=4.9

Set 3-Standard Deviation=1.7

Set 4-Standard Deviation=3.2

• Set 1

• Set 2

• Set 3

• Set 4

87 students were interviewed and classified according to their attitude toward school and the range their GPA falls in. The results are shown in the table below. Which of the following is true?

• The proportion of students with a neutral attitude towards school is larger than the proportion for students with a GPA in the 2.0 – 2.9 range.

• The students who had a 2.0 – 2.9 GPA given they had a neutral attitude towards school was smaller than the proportion of students who had a negative attitude given they were in the 2.0 – 2.9 GPA range.

• The proportion of students who had a positive attitude towards school and got a 3.0 – 3.9 GPA was the largest.

• The proportion of students who had a negative attitude towards school and got a 0.0 – 0.9 GPA was the smallest.

• More students had a positive attitude towards school than those that had a 3.0 – 3.9 GPA.

Which of the following statements is true?

• Values of r near 0 indicate a strong linear relationship.

• Changing the measurement units of x and y may affect the correlation between x and y.

• Strong correlation means that there is a definite cause-and-effect relationship between x and y.

• Correlation changes when the x and y variables are reversed.

• The correlation can be strongly affected by a few outlying observations.

Place the following four correlations in order from smallest to largest (hint: provide the correlation coefficient for each, then rank them smallest to largest):

• (A) II, IV, I, III

• (B) IV, III, I, II

• (C) IV, II, I, III

• (D) III, III, IV, I

• (E) II, IV, III, I

Which of the following best describes the correlation between two variables if r = 0.978?

• negative and weak

• positive and weak

• negative and strong

• positive and strong

• no correlation

The scatterplot below shows the fuel efficiency (in miles per gallon) and weight (in pounds) of 14 car models from 2022. What is the relationship between fuel efficiency and weight?

• As weight increases, fuel efficiency increases.

• As weight increases, fuel efficiency decreases.

• There is no relationship between weight and fuel efficiency.

• Fuel efficiency is constant regardless of weight.

The scatterplot below shows the fuel efficiency (in miles per gallon) and weight (in pounds) of 14 2022 car models. What is the relationship between fuel efficiency and weight?

• As weight increases, fuel efficiency increases.

• As weight increases, fuel efficiency decreases.

• There is no relationship between weight and fuel efficiency.

• Fuel efficiency is constant regardless of weight.

Response variable: __________________________

• Car Weight (Pounds)

• Country Road Fuel Efficiency (MPG)

Circle the following that is closest to the correlation between car weight and fuel efficiency for these vehicles. Explain why this makes sense in the context of the problem.

• r = -0.9

• r = -0.6

• r = 0.1

• r = 0.4

Explain why a correlation of r = -0.6 would make sense in the context of the fuel efficiency problem.

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