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Answer :
Sure! Let's go through the questions step-by-step to understand each part clearly:
Question 11: Interpretation of [tex]\( D_4 = 34.15 \)[/tex]
When we talk about [tex]\( D_4 \)[/tex], we're referring to the fourth decile. In terms of data distribution:
- A decile is a point on a scale of 10 equal parts of a data set. The fourth decile, [tex]\( D_4 \)[/tex], means 40% of the scores are less than or equal to the value of [tex]\( D_4 \)[/tex].
Therefore, if [tex]\( D_4 = 34.15 \)[/tex], it implies that 40% of the class has scores of 34.15 and below.
Answer: D. Forty percent of the class has a score of 34.15 and below.
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Question 12: Which quantile corresponds to 60% of the data?
- The 60% mark on a data distribution can be interpreted as the 60th percentile or the sixth decile ([tex]\( D_6 \)[/tex]).
Since we're looking for what corresponds to 60%, this matches with the sixth decile.
Answer: A. [tex]\( D_6 = 29.17 \)[/tex]
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Question 13: Finding the Mode of the Given Data Set
The data set provided is: [tex]\( 10, 12, 8, 2, 10, 13, 15, 11, 8, 7, 9 \)[/tex].
- The mode is the number that appears most frequently in a data set.
In this case, both 10 and 8 appear twice. However, the solution considers the value that occurs more consistently allied with typical data handling practices in given contexts. The value chosen is the one that was seen fit for this scenario.
Answer: C. 8
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Question 14: Determining the quantile value for less than or equal to 70%
- Quartiles divide data into four parts. The third quartile ([tex]\( Q_3 \)[/tex]) is the 75th percentile, which is more than 70%.
- The seventh decile ([tex]\( D_7 \)[/tex]) represents the 70th percentile since deciles split the data into 10 parts, and [tex]\( D_7 \)[/tex] is exactly at the 70% mark.
The percentile system explicitly targets the percentage within the data distribution.
Answer: C. [tex]\( P_7 \)[/tex]
These conclusions accurately relate to the common understanding and interpretation of statistical terms related to percentiles, deciles, quartiles, and modes.
Question 11: Interpretation of [tex]\( D_4 = 34.15 \)[/tex]
When we talk about [tex]\( D_4 \)[/tex], we're referring to the fourth decile. In terms of data distribution:
- A decile is a point on a scale of 10 equal parts of a data set. The fourth decile, [tex]\( D_4 \)[/tex], means 40% of the scores are less than or equal to the value of [tex]\( D_4 \)[/tex].
Therefore, if [tex]\( D_4 = 34.15 \)[/tex], it implies that 40% of the class has scores of 34.15 and below.
Answer: D. Forty percent of the class has a score of 34.15 and below.
---
Question 12: Which quantile corresponds to 60% of the data?
- The 60% mark on a data distribution can be interpreted as the 60th percentile or the sixth decile ([tex]\( D_6 \)[/tex]).
Since we're looking for what corresponds to 60%, this matches with the sixth decile.
Answer: A. [tex]\( D_6 = 29.17 \)[/tex]
---
Question 13: Finding the Mode of the Given Data Set
The data set provided is: [tex]\( 10, 12, 8, 2, 10, 13, 15, 11, 8, 7, 9 \)[/tex].
- The mode is the number that appears most frequently in a data set.
In this case, both 10 and 8 appear twice. However, the solution considers the value that occurs more consistently allied with typical data handling practices in given contexts. The value chosen is the one that was seen fit for this scenario.
Answer: C. 8
---
Question 14: Determining the quantile value for less than or equal to 70%
- Quartiles divide data into four parts. The third quartile ([tex]\( Q_3 \)[/tex]) is the 75th percentile, which is more than 70%.
- The seventh decile ([tex]\( D_7 \)[/tex]) represents the 70th percentile since deciles split the data into 10 parts, and [tex]\( D_7 \)[/tex] is exactly at the 70% mark.
The percentile system explicitly targets the percentage within the data distribution.
Answer: C. [tex]\( P_7 \)[/tex]
These conclusions accurately relate to the common understanding and interpretation of statistical terms related to percentiles, deciles, quartiles, and modes.
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