Math 1 Statistics Review

The following boxplot shows the heights of students in Kyra’s Health class. Which measures of center spread should be used to describe it?

• Mean and Standard Deviation because the shape of the data is normal.

• Mean and IQR because the shape of the data is normal.

• Median and Standard Deviation because the shape of the data is skewed.

• Median and IQR because the shape of the data is skewed.

Answer explanation

When data is normal in shape, we use the mean and standard deviation to describe it because there are no really high or really low data value skewing the data in one direction.

In the data set shown, how would adding a 200 change the mean and median?

14, 15, 16, 17, 18, 19

• The mean would increase a lot, the median would increase only a little.

• The mean and median would both increase a lot.

• The median would increase a lot, the mean would increase only a little.

• The mean and median would stay the same.

Answer explanation

Adding a really big outlier causes the mean to increase, but it doesn't really affect the median at all.

Ms. Michaelson drew a box and whisker plot to represent her students’ scores on a recent math test.

If Jennifer scored an 86 on her test, how does she compare to the rest of the students in her class?

• Jennifer scored in the top 25% of her class.

• There is no way of knowing how Jennifer did compared to the rest of her class.

• There were not a lot of students who scored between 85 and 95 because the whisker on the higher end of the data is shorter.

Answer explanation

A box and whisker plot uses the five number summary to split data into four sections, each containing 25% of the data. Since Jennifer scored an 86, that puts her in the top 25%.

The boxplots below show test scores from Mr. Payne’s 1^st and 2^nd period classes.

Which class typically performed better?

• First period

• Second period

Answer explanation

Second period performed better because the data is less spread out, meaning their scores were more consistently higher than first period.

The data below represent the number of absences and the final grade of 9 randomly selected students from a Math 1 class. The data shows what type of correlation?

• Negative Correlation

• Positive Correlation

Answer explanation

Looking at the scatterplot, the points go down from left to right resulting in a negative correlation. Also - having more absences would cause your grade to decrease.

The data below represent the number of absences and the final grade of 9 randomly selected students from a Math 1 class. Find the equation for the line of best fit. 

•  $y=-2.95x+96.12$  

•  $y=96.12x-2.95$  
  

•  $y=1x+1$  

Answer explanation

Did you miss this question? Is the data typed correctly into line 1 of Desmos? Check it, because you will use this data again on other questions!

The data below represent the number of absences and the final grade of 9 randomly selected students from a Math 1 class. The correlation coefficient for this data is -.94. What does this tell you?

• There is a strong negative correlation.

• There is a strong positive correlation.

• There is a weak negative correlation.

• There is a weak positive correlation.

Answer explanation

The correlation coefficient tells you strength and direction. The closer to 1 or -1, the stronger the correlation!

The data below represent the number of absences and the final grade of 9 randomly selected students from a Math 1 class. 

You are asked to predict the final grade for a student with 20 absences. This prediction is an example of...

• Interpolation

• Extrapolation

Answer explanation

Since 20 falls outside the range of absences shown in the table, this is an example of extrapolation.

The data below represent the number of absences and the final grade of 9 randomly selected students from a Math 1 class. Predict the final grade for a student who has 20 absences.

Answer explanation

Did you miss this question? With the line of best fit still showing on your graph, type "x=20" in an empty line. Click on the intersection, what is the y-value?

The graph shown is the residual plot for the Number of Absences vs. Final Grade data. What does this tell you?

• There is no pattern, so a linear model is appropriate.

• There is no correlation.

• There is no pattern, so a linear model is not appropriate.

• Something is wrong here... I thought you couldn't have a negative grade! Oh boy.. I'm in trouble!

Answer explanation

Remember: When it comes to residual plots, NO pattern is GOOD. It means the linear model is appropriate. If you can see a curve, "u" shape or line, that means the linear model is not appropriate.