Common Core: 6th Grade Math : Understand the Shape of a Data Set: CCSS.Math.Content.6.SP.B.5d

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

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Example Questions

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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:

Median

Either mode or mean 

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:

Either range or interquartile range

Neither range nor interquartile range 

Interquartile range

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 #3 : 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:

Either mean or median 

Mean

Mode

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 #4 : 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:

Range

Either range or interquartile range

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. 

Example Question #5 : 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:

Either range or interquartile range

Neither range nor interquartile range 

Range

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 #6 : 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 12.56.21 pm

Possible Answers:

Either mode or median 

Median

Mean

Mode

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:

There is no mode for this set because each value only appears once.

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: None 

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 of how varied the set is. Normally, when a data set is varied the mean is normally the best measure of center.

Example Question #7 : 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 1.15.23 pm

Possible Answers:

Interquartile range

Neither range nor interquartile range 

Either range or interquartile range

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 #8 : 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 1.15.23 pm

Possible Answers:

Mode

Median

Either the median or the mode

Mean

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 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 of how varied the set is. Normally, when a data set is varied the mean is normally the best measure of center.

Example Question #9 : 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 1.33.12 pm

Possible Answers:

Either median or mode

Median

Mode

Mean

Correct answer:

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 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. In this data set we have an outlier, which means the mean is not going to be the best measure of center. Also, the mode is the lowest value in our set; thus, the median is the best measure of center. 

Example Question #10 : 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 1.33.12 pm

Possible Answers:

Range

Either range or interquartile range

Neither range nor interquartile range 

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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