Respuesta :
Answer:
The IQR of mid-terme exams is the largest.
Step-by-step explanation:
Calculating the IQR of Mid-Term exams
Considering the Mid term numbers
[tex]100\:100\:100\:95\:95\:92\:92\:88\:85\:75[/tex]
Median [tex]=\frac{95+92}{2}[/tex]
[tex]=\frac{187}{2}[/tex]
= [tex]93.5[/tex]
As the first quarter = [tex]Q1[/tex] = [tex]100\:100\:100\:95[/tex]
Median of first quarter = [tex]\frac{\left(100\:+\:100\right)}{2}[/tex]
[tex]= 100[/tex]
Third quarter = [tex]Q3[/tex] = [tex]92\:88\:85\:75[/tex]
Median of third quarter [tex]=\frac{88+85}{2}[/tex]
[tex]=86.5[/tex]
As we know that
Interquartile range (IQR) can be computed by subtracting Q3 from Q1.
So,
IQR of mid-term exams = [tex]86.5 - 100[/tex]
= [tex]-13.5[/tex]
Calculating the IQR of Final exams
Considering the Final term numbers
[tex]98\:95\:93\:91\:88\:82\:78\:78\:65\:60[/tex]
Median [tex]=\frac{88+82}{2}[/tex]
[tex]=85[/tex]
As the first quarter = [tex]Q1[/tex] = [tex]98\:95\:91\:88[/tex]
Median of first quarter = [tex]\frac{\left(95\:+\:91\right)}{2}[/tex]
= [tex]93[/tex]
Third quarter = [tex]Q3[/tex] = [tex]78\:78\:65\:60[/tex]
Median of third quarter [tex]=\frac{78+65}{2}[/tex]
= [tex]71.5[/tex]
Interquartile range (IQR) can be computed by subtracting Q3 from Q1.
So,
IQR of final-term exams = [tex]71.5 -93[/tex]
= [tex]-21.5[/tex]
Therefore, the IQR of mid-term exams is the largest.
Keywords: Interquartile range (IQR), Median
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Answer:
Final Exam
This is the results for Final Exam
Population size: 10
Median: 85
Minimum: 60
Maximum: 98
First quartile: 74.75
Third quartile: 93.5
Interquartile Range: 18.75
Outliers: none
And This is the results for the Midterm
Population size: 10
Median: 93.5
Minimum: 75
Maximum: 100
First quartile: 87.25
Third quartile: 100
Interquartile Range: 12.75
Outliers: none
