Common Core: 6th Grade Math : Statistics & Probability

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #1495 : Grade 6

Mrs. Hobb's  grade class just completed a fundraiser to help fund their field trips for this school year. The money that the students sold is displayed in the histogram provided. What is the the unit of measurement in this chart?


2

Possible Answers:

Cents

Money

Hours

Dollars

Correct answer:

Dollars

Explanation:

To answer this question correctly, we need to look at the histogram. The teacher is tracking dollars that each student made through the fundraiser; thus, the correct answer is dollars. 

Example Question #72 : Statistics & Probability

Mrs. Hobb's  grade class just completed a fundraiser to help fund their field trips for this school year. The money that the students sold is displayed in the histogram provided. How many students made sales during the fundraiser?

 


2

Possible Answers:

Correct answer:

Explanation:

For this plot, the number of observations made represents the number of students that participated in the made money through the fundraiser. Each bar goes up to a certain number of students, so we can add up the height of each bar to determine the number of observations that were made.

If done correctly,  we should have found that  students fundraised. 

Example Question #1 : Find Measures Of Center, Variability, And Patterns In Data: Ccss.Math.Content.6.Sp.B.5c

Subtract the mode from the median in this set of numbers:

9080, 9008, 9800, 9099, 9009, 9090, 9008

Possible Answers:

Correct answer:

Explanation:

First, order the numbers from least to greatest:

Then, find the mode (the most recurring number): 9008

Then, find the median (the middle number):

Finally, subtract the mode from the median:

Answer: 72.

Example Question #4 : How To Find Median

Consider the data set: 

What is the difference between the mean of this set and the median of this set?

Possible Answers:

Correct answer:

Explanation:

To get the mean, add the numbers and divide by 8:

To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle):

The difference is 

Example Question #1 : Find Measures Of Center, Variability, And Patterns In Data: Ccss.Math.Content.6.Sp.B.5c

The difference between 2996 and 4515 is closest to 

Possible Answers:

Correct answer:

Explanation:

Round 2996 up to 3000 and 4515 down to 4500.  The difference between 4500 and 3000 is 1500.

Example Question #1 : Understand The Shape Of A Data Set: Ccss.Math.Content.6.Sp.B.5d

Which of the following is the best measure of center for the data set in the provided table?

Screen shot 2016 04 05 at 10.19.45 am

Possible Answers:

Either mode or mean 

Median

Mode

Either mode or median

Correct answer:

Either mode or median

Explanation:

In order to answer this question correctly, we need to solve for the mean, median, and mode of this data set. 

To begin, let's sort the data from least to greatest:

Now that our data is ordered from least to greatest, we can solve for the median:

Remember, the median is the middle most number when a data set is ordered from least to greatest.

The median for this data set is 

Next, we can look at our data set to determine the mode:

The mode for this data set is 

Remember, the mode is the number in a set that appears most often. 

Finally, we can solve for the mean:

 

Remember, the mean of a data set is the average of the numbers in a data set. 

The mean for this data set is 

Now that we've done our calculation we should have:

Median: 

Mode:  

Mean: 

We are looking for the value that is representative of the center of the data; thus the mode or median would be the best measurement to use. 

Example Question #2 : Understand The Shape Of A Data Set: Ccss.Math.Content.6.Sp.B.5d

Which of the following is the best measure of variability for the data in the provided table?

Screen shot 2016 04 05 at 10.19.45 am

Possible Answers:

Range

Interquartile range

Neither range nor interquartile range 

Either range or interquartile range

Correct answer:

Interquartile range

Explanation:

In order to answer this question correctly, we need to solve for the range and the interquartile range. 

To begin, let's sort the data from least to greatest:

Next, we can solve for the range. Remember, the range of a data set is the difference between the highest value and the lowest value in the set. 

The range for this data set is 

Now, we can solve for the interquartile range. Remember, the interquartile range is the difference between the upper quartile median and the lower quartile median. This means that we need to first calculate these two values. In order to do this, we need to split the data set into quartiles. 

First, we will find the median:

We will then use the median to split the data in half. Next,  we must find the median of the first half—or lower quartile—and then the median of the second half—or upper quartile:

Now we can solve for the difference between the upper quartile median and the lower quartile median:

Now that we have completed these operations, we should have calculated the following values:

Range: 

Interquartile range: 

As you can see, solving for the interquartile range requires more steps because it takes into account more of the data points; thus, given our options, interquartile range is best to use when solving for variability. 

Example Question #2 : Understand The Shape Of A Data Set: Ccss.Math.Content.6.Sp.B.5d

Which of the following is the best measure of center for the data set in the provided table?

Screen shot 2016 04 05 at 12.14.34 pm

Possible Answers:

Mode

Mean

Either mean or median 

Median

Correct answer:

Mean

Explanation:

In order to answer this question correctly, we need to solve for the mean, median, and mode of this data set. 

To begin, let's sort the data from least to greatest:

Now that our data is ordered from least to greatest, we can solve for the median:

Remember, the median is the middle most number when a data set is ordered from least to greatest.

The median for this data set is 

Next, we can look at our data set to determine the mode:

The mode for this data set is 

Remember, the mode is the number in a set that appears most often. 

Finally, we can solve for the mean:

 

Remember, the mean of a data set is the average of the numbers in a data set. 

The mean for this data set is 

Now that we've done our calculation we should have:

Median: 

Mode:  

Mean: 

We are looking for the value that is representative of the center of the data; thus the mean would be the best measure because  and  represent the greatest values of our data set, but  is more reflective of the center of all of the values. Normally, when a data set is varied the mean is normally the best measure of center. 

Example Question #3 : Understand The Shape Of A Data Set: Ccss.Math.Content.6.Sp.B.5d

Which of the following is the best measure of variability for the data in the provided table?

Screen shot 2016 04 05 at 12.14.34 pm

Possible Answers:

Neither range nor interquartile range 

Interquartile range

Range

Either range or interquartile range

Correct answer:

Interquartile range

Explanation:

In order to answer this question correctly, we need to solve for the range and the interquartile range. 

To begin, let's sort the data from least to greatest:

Next, we can solve for the range. Remember, the range of a data set is the difference between the highest value and the lowest value in the set. 

The range for this data set is 

Now, we can solve for the interquartile range. Remember, the interquartile range is the difference between the upper quartile median and the lower quartile median. This means that we need to first calculate these two values. In order to do this, we need to split the data set into quartiles. 

First, we will find the median:

We will then use the median to split the data in half. Next,  we must find the median of the first half—or lower quartile—and then the median of the second half—or upper quartile:

Now we can solve for the difference between the upper quartile median and the lower quartile median:

Now that we have completed these operations, we should have calculated the following values:

Range: 

Interquartile range: 

As you can see, solving for the interquartile range requires more steps because it takes into account more of the data points; thus, given our options, interquartile range is best to use when solving for variability. 

Example Question #2 : Understand The Shape Of A Data Set: Ccss.Math.Content.6.Sp.B.5d

Which of the following is the best measure of variability for the data in the provided table?

Screen shot 2016 04 05 at 12.56.21 pm

Possible Answers:

Range

Interquartile range

Either range or interquartile range

Neither range nor interquartile range 

Correct answer:

Interquartile range

Explanation:

In order to answer this question correctly, we need to solve for the range and the interquartile range. 

To begin, let's sort the data from least to greatest:

Next, we can solve for the range. Remember, the range of a data set is the difference between the highest value and the lowest value in the set. 

The range for this data set is 

Now, we can solve for the interquartile range. Remember, the interquartile range is the difference between the upper quartile median and the lower quartile median. This means that we need to first calculate these two values. In order to do this, we need to split the data set into quartiles. 

First, we will find the median:

We will then use the median to split the data in half. Next,  we must find the median of the first half—or lower quartile—and then the median of the second half—or upper quartile:

Now we can solve for the difference between the upper quartile median and the lower quartile median:

Now that we have completed these operations, we should have calculated the following values:

Range: 

Interquartile range: 

As you can see, solving for the interquartile range requires more steps because it takes into account more of the data points; thus, given our options, interquartile range is best to use when solving for variability. 

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