If Qi​, Di​, and Pi​ refer respectively to the i-th quartile, i-th decile, and i-th percentile, which of the following measures represents the correct relationship between them?

Correct option is C

To understand the relationship between quartiles, deciles, and percentiles, let’s break down each term:
1. Quartile (Qi): Divides the data into four equal parts.
· Q1​: 25th percentile
· Q2​: 50th percentile (Median)
· Q3​: 75th percentile
2. Decile (Di​): Divides the data into ten equal parts.
· D5​: 50th percentile (Median)
3. Percentile (Pi​): Divides the data into 100 equal parts.
· P50​: The 50th percentile (Median)
Thus, the relationship:
Q2=P50=D5
indicates the median of the dataset, representing the point where 50% of the data lies below it.
Information Booster:
1. Quartiles:
· Q1​ = 25th percentile
· Q2 = 50th percentile (Median)
· Q3​ = 75th percentile
2. Deciles:
· D1​ = 10th percentile
· D2 = 20th percentile
· D5​ = 50th percentile (Median)
3. Percentiles:
· P10 = 10th percentile
· P25 ​ = 25th percentile (Same as Q1)
· P50 ​ = 50th percentile (Same as Q2​ and D5​)
4. Median:
· The median is the middle value when the data is sorted, equivalent to the 50th percentile, Q2Q_2Q2​, and D5D_5D5​.
Additional Knowledge:
· Interquartile Range (IQR):
· IQR = Q3−Q1
· Measures the spread of the middle 50% of the data.
· Uses of Quartiles, Deciles, and Percentiles:
· Quartiles: Used for understanding data distribution and calculating IQR.
· Deciles: Often used in educational assessments or economic data.
· Percentiles: Common in standardized tests and health assessments (e.g., child growth charts).
Example:
If a dataset of exam scores is sorted, and the score corresponding to the middle is 75:
· 75 is the Median (Q2​),
· 75 is also the 50th Percentile (P50​),
· 75 is the 5th Decile (D5​).