# Section 6.4 - Reasoning About Data

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| By Seixeiroda
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Complete the following questions

• 1.

### A data set the shows no clear trend or pattern can be used to

• A.

Write a conjecture

• B.

Support a conjecture

• C.

Reject a conjecture

• D.

Find an outlier

C. Reject a conjecture
Explanation
If a data set shows no clear trend or pattern, it means that there is no consistent relationship or correlation between the variables being studied. In this case, it would not be appropriate to support or write a conjecture based on the data set, as there is no evidence or indication to support any particular claim or hypothesis. Therefore, the correct answer is to reject a conjecture, as there is no basis for making any assumptions or conclusions about the data set.

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• 2.

### Which of these lines or curves of best fit would support a conjecture that as outside temperature increases, the fewer people go to the athletic club

• A.

A line of best fit that shows a positive slope

• B.

A line of best fit that shows a negative slope

• C.

A line of best fit that shows a zero slope

• D.

A curve of best fit that shows a slight upward curve

B. A line of best fit that shows a negative slope
Explanation
A line of best fit that shows a negative slope would support the conjecture that as outside temperature increases, fewer people go to the athletic club. This means that as the temperature increases, the number of people going to the athletic club decreases. The negative slope indicates a negative correlation between temperature and the number of people going to the club.

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• 3.

### Keren used the data in the table to make a conjecture about whether starting teacher salary and the amount spent per pupil are related.  To assure that her conjecture is valid, what should Keren do?

• A.

Rewrite her conjecture to include the outlier

• B.

Extend the curve of best fit

• C.

Use a line of best fit instead of a curve

• D.

Gather more data

D. Gather more data
Explanation
To assure that her conjecture is valid, Keren should gather more data. This is because having a larger sample size can help to improve the accuracy and reliability of any statistical analysis or conclusions drawn from the data. By collecting more data, Keren can have a more comprehensive understanding of the relationship between starting teacher salary and the amount spent per pupil, and thus validate or refine her conjecture.

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• 4.

### When is it not valid to use the line of best fit to make prdications about the general population?

• A.

When the data set is small

• B.

When the data shows a smooth curve

• C.

When there is an outlier

• D.

When there is a negative slope

A. When the data set is small
Explanation
When the data set is small, it may not be representative of the entire population, and therefore using a line of best fit to make predictions about the general population would not be valid. A small data set may not capture the full range of variability and trends present in the population, leading to inaccurate predictions.

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• 5.

### To support a conjecture, a plot must show which of the following?1) A positive correlation 2) A negatice correlation 3) A trend or pattern

• A.

1 only

• B.

2 only

• C.

3 only

• D.

1, 2, and 3

C. 3 only
Explanation
To support a conjecture, a plot must show a trend or pattern. A trend or pattern in the data helps to establish a relationship or connection between the variables being studied. A positive or negative correlation is a specific type of trend or pattern, but it is not necessary for a plot to show a correlation in order to support a conjecture. Therefore, the correct answer is 3 only, as it encompasses the essential requirement for supporting a conjecture.

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• 6.

### Rebecca collected this data of the math grades of grade 9 students and the number of siblings each student has.  What conjecture is supported by the data?

• A.

People with fewer siblings do better in math

• B.

People with 3 or more siblings do worse in math

• C.

People with no siblings do the best in math

• D.

People with more siblings do better in math

D. People with more siblings do better in math
Explanation
The given data supports the conjecture that people with more siblings do better in math. This can be inferred from the fact that Rebecca collected data on the math grades of grade 9 students and the number of siblings each student has. By analyzing the data, it is likely that students with more siblings had higher math grades on average.

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• 7.

### Which conjecture is supported by the data?

• A.

The shorter the time between eruptions, the longer the eruption

• B.

The longer the time between eruptions, the longer the eruption

• C.

The longer the time between eruptions, the shorter the eruption

• D.

The time between eruptions remains constant, regardless of the length of the eruption.

B. The longer the time between eruptions, the longer the eruption
Explanation
The data supports the conjecture that the longer the time between eruptions, the longer the eruption. This means that there is a positive correlation between the length of time between eruptions and the duration of the eruption.

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• 8.

### Suppose that you plot two variables on a scatter plot, and then draw a curve of best fit.  What does it mean if the curve faces downward?

• A.

The data show no relation

• B.

The data contradict the conjecture

• C.

There is not enough data

• D.

The data show an inverse relationship

D. The data show an inverse relationship
Explanation
If the curve of best fit faces downward on a scatter plot, it means that there is an inverse relationship between the two variables being plotted. This means that as one variable increases, the other variable decreases. The data points on the scatter plot follow a pattern where higher values of one variable correspond to lower values of the other variable.

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• 9.

### What is the relationship between the variables

• A.

As temperature increases, the number of chirps decreases

• B.

The number of chirps remains constant regardless of temperature

• C.

The number of chirps increases as temperature increases

• D.

There is no relationship between the variables

C. The number of chirps increases as temperature increases
Explanation
The correct answer is that the number of chirps increases as temperature increases. This suggests that there is a positive correlation between temperature and the number of chirps. As the temperature rises, the chirping of the insects also increases. This relationship implies that temperature plays a role in the behavior or physiology of the chirping insects, causing them to chirp more frequently when it is warmer.

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• 10.

### Which point is an outlier for the data set?

• A.

(16, 0.86)

• B.

(1.2, 0.94)

• C.

(114, 0.16)

• D.

(87.6, 1.1)

D. (87.6, 1.1)
Explanation
The point (87.6, 1.1) is an outlier for the data set because it is significantly different from the other data points. The x-value of 87.6 is much larger than the other x-values, and the y-value of 1.1 is also larger compared to the other y-values. This point does not follow the general trend of the data and is considered an anomaly.

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