Different? Third sentence Range: 23 Interquartile Range: 9
Practice makes perfect
The set of numbers used to draw a box-and-whisker plot are, in order from left to right, the least value, first quartile, median, third quartile, and greatest value. These are called the five-number summary of the data set. Let's consider the given box-and-whisker plot.
In this case, the five-number summary of the data is already marked on the graph. Let's write it in a table.
Five-Number Summary
Least Value
1
First Quartile (Q_1)
11
Median
15
Third Quartile (Q_3)
20
Greatest Value
24
With these values in mind, we can analyze each given sentence. Then, we will compare it to find which is different.
First Sentence
The first sentence asked us to find the interquartile range of the data. The interquartile range is the difference between the third and first quartiles of the data.
IQR:Q_3-Q_1 ⇒ IQR:20-11= 9
Therefore, the interquartile range is 9.
Second Sentence
This sentence asked to find the range of the middle half of the data. Since quartiles divide the data into four equal parts, the middle half of the data is between the first and third quartiles. This means that the range of the middle half will be the difference between the third and first quartiles.
Q_3-Q_1& =20-11
& = 9
In this sentence, we are actually calculating the interquartile range of the data.
Third Sentence
In this sentence, we are asked to find the difference between the greatest and least values of the data set. This is the definition of range. Let's find it!
Range:24-1= 23
The range of the data is 23.
Fourth Quartile
This sentence asked to find the difference between the third and first quartiles of the data, which is the interquartile range. Once again, this is 20-11= 9.
Conclusion
The first, second, and fourth sentences asked for the interquartile range of the data. The third sentence asked for the range of the data.
IQR:& 9
Range:& 23
Therefore, the third sentence is the one that is different.
