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
All Common Core: 6th Grade Math Resources
Example Questions
Example Question #11 : 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?
Either mode or median
Median
Mean
Mode
Median
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 #11 : 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?
Range
Interquartile range
Neither range nor interquartile range
Either range or interquartile range
Interquartile range
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.
All Common Core: 6th Grade Math Resources
