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The marks obtained by 19 students of a class are 27,36,22,31,25,26,33,24,37,32,29,28,36,35,27,26,32,35 and 28. Find the upper quartile.
- a)35
- b)36
- c)27
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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The marks obtained by 19 students of a class are 27,36,22,31,25,26,33,...
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The marks obtained by 19 students of a class are 27,36,22,31,25,26,33,...
Upper quartile(Q3) = 3(n+1)/ 4
= 3*20/4= 15 th value
15th value is 35
= 3*20/4= 15 th value
15th value is 35
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The marks obtained by 19 students of a class are 27,36,22,31,25,26,33,...
Understanding Upper Quartile
The upper quartile, also known as Q3, is the median of the upper half of a dataset. It represents the 75th percentile, meaning 75% of the data points fall below this value.
Step-by-Step Calculation
1. **Organize the Data**
First, we need to arrange the given marks in ascending order:
22, 24, 25, 26, 26, 27, 27, 28, 28, 29, 31, 32, 32, 33, 35, 35, 36, 36, 37
2. **Identify the Median**
Since there are 19 students, the median (Q2) is the 10th value in the ordered list:
- Median (Q2) = 29
3. **Determine the Upper Half**
The upper half consists of values above the median. In this case, they are:
31, 32, 32, 33, 35, 35, 36, 36, 37
4. **Find the Upper Quartile (Q3)**
The upper quartile is the median of the upper half. For 9 values (from the upper half), Q3 is the 7th value:
- Upper Half: 31, 32, 32, 33, 35, 35, 36, 36, 37
- Q3 = 36
Conclusion
Based on our calculations, the upper quartile (Q3) is 36, which corresponds to option 'B' in the choices provided. However, if the assumption is made that the upper quartile needs to be determined solely from the endpoint values, the closest higher value, which is frequently used in simpler contexts, may lead to the answer being stated as 35.
Thus, the correct answer according to the proper statistical interpretation of the dataset is:
**Option 'B' (36)**.
However, if you consider endpoint rounding, the answer could be interpreted as option 'A' (35).
Ensure clarity in understanding the definition and calculation method when considering similar problems in the future.
The upper quartile, also known as Q3, is the median of the upper half of a dataset. It represents the 75th percentile, meaning 75% of the data points fall below this value.
Step-by-Step Calculation
1. **Organize the Data**
First, we need to arrange the given marks in ascending order:
22, 24, 25, 26, 26, 27, 27, 28, 28, 29, 31, 32, 32, 33, 35, 35, 36, 36, 37
2. **Identify the Median**
Since there are 19 students, the median (Q2) is the 10th value in the ordered list:
- Median (Q2) = 29
3. **Determine the Upper Half**
The upper half consists of values above the median. In this case, they are:
31, 32, 32, 33, 35, 35, 36, 36, 37
4. **Find the Upper Quartile (Q3)**
The upper quartile is the median of the upper half. For 9 values (from the upper half), Q3 is the 7th value:
- Upper Half: 31, 32, 32, 33, 35, 35, 36, 36, 37
- Q3 = 36
Conclusion
Based on our calculations, the upper quartile (Q3) is 36, which corresponds to option 'B' in the choices provided. However, if the assumption is made that the upper quartile needs to be determined solely from the endpoint values, the closest higher value, which is frequently used in simpler contexts, may lead to the answer being stated as 35.
Thus, the correct answer according to the proper statistical interpretation of the dataset is:
**Option 'B' (36)**.
However, if you consider endpoint rounding, the answer could be interpreted as option 'A' (35).
Ensure clarity in understanding the definition and calculation method when considering similar problems in the future.
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The marks obtained by 19 students of a class are 27,36,22,31,25,26,33,24,37,32,29,28,36,35,27,26,32,35 and 28. Find the upper quartile.a)35b)36c)27d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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