Question 1205202: 1. Considering the following distribution for blood pressure level of male patients in a given hospital
(in mm Hg).
Values (BP) Frequency (# of patients)
140- 150 17
150- 160 29
160- 170 42
170- 180 72
180- 190 84
190- 200 107
200- 210 49
210- 220 34
220- 230 31
230- 240 16
240- 250 12
Calculate:
a) All the quartiles.
b) Find the 8th deciles.
c) Find the 20th percentiles
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To calculate the quartiles, deciles, and percentiles, we first need to create a cumulative frequency distribution table:
| Blood Pressure (BP) | Frequency (f) | Cumulative Frequency (cf) |
|---|---|---|
| 140-150 | 17 | 17 |
| 150-160 | 29 | 46 |
| 160-170 | 42 | 88 |
| 170-180 | 72 | 160 |
| 180-190 | 84 | 244 |
| 190-200 | 107 | 351 |
| 200-210 | 49 | 400 |
| 210-220 | 34 | 434 |
| 220-230 | 31 | 465 |
| 230-240 | 16 | 481 |
| 240-250 | 12 | 493 |
**Total Frequency (N) = 493**
### a) Quartiles
* **Q1 (First Quartile):**
* Position of Q1 = N/4 = 493/4 ≈ 123.25
* Q1 lies in the 4th class interval (170-180).
* Using interpolation, Q1 = 170 + [(123.25 - 88) / 72] * 10 ≈ 175.18
* **Q2 (Second Quartile or Median):**
* Position of Q2 = N/2 = 493/2 ≈ 246.5
* Q2 lies in the 6th class interval (190-200).
* Using interpolation, Q2 = 190 + [(246.5 - 244) / 107] * 10 ≈ 190.23
* **Q3 (Third Quartile):**
* Position of Q3 = 3N/4 = 3*493/4 ≈ 369.75
* Q3 lies in the 7th class interval (200-210).
* Using interpolation, Q3 = 200 + [(369.75 - 351) / 49] * 10 ≈ 203.78
### b) 8th Decile
* Position of the 8th decile = 8N/10 = 8*493/10 ≈ 394.4
* The 8th decile lies in the 7th class interval (200-210).
* Using interpolation, 8th decile = 200 + [(394.4 - 351) / 49] * 10 ≈ 208.86
### c) 20th Percentile
* Position of the 20th percentile = 20N/100 = 20*493/100 ≈ 98.6
* The 20th percentile lies in the 3rd class interval (160-170).
* Using interpolation, 20th percentile = 160 + [(98.6 - 88) / 42] * 10 ≈ 162.52
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