Partition Values **What are partition values?** Partition values are values that divide a distribution into equal parts. Common partition values include quartiles (dividing into 4 parts), deciles (dividing into 10 parts), and percentiles (dividing into 100 parts). **From the following distribution o
Partition Values
What are partition values?
Partition values are values that divide a distribution into equal parts. Common partition values include quartiles (dividing into 4 parts), deciles (dividing into 10 parts), and percentiles (dividing into 100 parts).
From the following distribution of scores of 200 students of a college, compute:
| Scores | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
|---|---|---|---|---|---|---|
| Number of students | 14 | 50 | 60 | 45 | 20 | 11 |
i. The minimum scores obtained by top 10% students.
The top 10% corresponds to the 90th percentile. We need to find the score below which 90% of students fall.
Position of 90th percentile = $\frac{90}{100} \times 200 = 180$
Cumulative frequencies:
- 30-40: 14
- 40-50: 64
- 50-60: 124
- 60-70: 169
- 70-80: 189
- 80-90: 200
The 180th student falls in the 70-80 class.
Using the formula: $P_{90} = L + \frac{\frac{90N}{100} - CF}{f} \times h$
$$P_{90} = 70 + \frac{180 - 169}{20} \times 10 = 70 + \frac{11}{20} \times 10 = 70 + 5.5 = 75.5$$
The minimum score obtained by top 10% students is 75.5
ii. The range of middle 60% students.
The middle 60% corresponds to the 20th to 80th percentiles.
For 20th percentile: Position = $\frac{20}{100} \times 200 = 40$
The 40th student falls in the 40-50 class.
$$P_{20} = 40 + \frac{40 - 14}{50} \times 10 = 40 + \frac{26}{50} \times 10 = 40 + 5.2 = 45.2$$
For 80th percentile: Position = $\frac{80}{100} \times 200 = 160$
The 160th student falls in the 60-70 class.
$$P_{80} = 60 + \frac{160 - 124}{45} \times 10 = 60 + \frac{36}{45} \times 10 = 60 + 8 = 68$$
The range of middle 60% students is 45.2 to 68
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Partition values are values that divide a distribution (arranged in order) into a number of equal parts. Common ones: - Quartiles ($Q$): divide data into 4 equal parts - Deciles ($D$): divide data into 10 equal parts - Percentiles ($P$): divide data into 100 equal parts Scores $f$ $cf$ ----------...