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What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3...
Understanding Interquartile Range
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. It helps to understand the spread of the middle 50% of the data.
Step 1: Organize the Data
First, we need to sort the data in ascending order:
- Original Data: 2, 1, 0, 3, 1, 2, 3, 4, 3, 5
- Sorted Data: 0, 1, 1, 2, 2, 3, 3, 3, 4, 5
Step 2: Find Q1 and Q3
- Finding Q1: The first quartile (Q1) is the median of the first half of the data.
- Data for Q1: 0, 1, 1, 2, 2
- Median of this half (middle value): 1
- Finding Q3: The third quartile (Q3) is the median of the second half of the data.
- Data for Q3: 3, 3, 4, 5
- Median of this half (middle value): 3
Step 3: Calculate the IQR
- IQR Calculation:
- IQR = Q3 - Q1
- IQR = 3 - 1 = 2
Conclusion
The interquartile range for the given dataset is 2, which corresponds to option 'B'. This value indicates the range within which the central 50% of the data points lie, providing a useful measure of spread while minimizing the influence of outliers.
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. It helps to understand the spread of the middle 50% of the data.
Step 1: Organize the Data
First, we need to sort the data in ascending order:
- Original Data: 2, 1, 0, 3, 1, 2, 3, 4, 3, 5
- Sorted Data: 0, 1, 1, 2, 2, 3, 3, 3, 4, 5
Step 2: Find Q1 and Q3
- Finding Q1: The first quartile (Q1) is the median of the first half of the data.
- Data for Q1: 0, 1, 1, 2, 2
- Median of this half (middle value): 1
- Finding Q3: The third quartile (Q3) is the median of the second half of the data.
- Data for Q3: 3, 3, 4, 5
- Median of this half (middle value): 3
Step 3: Calculate the IQR
- IQR Calculation:
- IQR = Q3 - Q1
- IQR = 3 - 1 = 2
Conclusion
The interquartile range for the given dataset is 2, which corresponds to option 'B'. This value indicates the range within which the central 50% of the data points lie, providing a useful measure of spread while minimizing the influence of outliers.
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Community Answer
What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3...
The given data in ascending order is 0, 1, 1, 2, 2, 3, 3, 3, 4, 5
n = 10 (even)
Lower quartile = n/4 th = 10/4th = 2.5th
= 3rd term
= 1
n = 10 (even)
Lower quartile = n/4 th = 10/4th = 2.5th
= 3rd term
= 1
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What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the interquartile range for the data 2, 1, 0, 3, 1, 2, 3, 4, 3, 5?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
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