Math Statistics Review

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

• 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.

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 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.

Calculate the standard deviation of the following set of numbers: 4, 8, 8, 10, 12.

• 2.83

• 3

• 3.16

The mean of a dataset is 20, and the standard deviation is 4. What is the z-score of a data point that is 24?

• 1

• 10

• 0

• 4

Find the coefficient of variation for a data set with a mean of 20 and a standard deviation of 5.

• 25%

• 20%

• 15%

• 10%

What kind of correlation?

• Positive

• Negative

• No Correlation

How many students scored between a 86 and a 90?

• 1

• 3

• 6

• 10

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.