Advertisements
Advertisements
प्रश्न
Calculate D9 and P20 of the following distribution.
| Length (in inches) | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 | 100 – 120 |
| No. of units | 1 | 14 | 35 | 85 | 90 | 15 |
Advertisements
उत्तर
We construct the less than cumulative frequency table as given below:
| Length (in inches) | No. of units (f) | Less than Cumulative frequency (c.f.) |
| 0 – 20 | 1 | 1 |
| 20 – 40 | 14 | 15 |
| 40 – 60 | 35 | 50 ← P20 |
| 60 – 80 | 85 | 135 |
| 80 – 100 | 90 | 225 ← D9 |
| 100 – 120 | 15 | 240 |
| Total | 240 |
Here, N = 240
D9 class = class containing `((9"N")/10)^"th"` observation
∴ `(9"N")/(10) = (9 xx 240)/(10)` = 216
Cumulative frequency which is just greater than (or equal to) 216 is 225
∴ D9 lies in the class 80 – 100.
∴ L = 80, f = 90, c.f. = 135, h = 20
∴ D9 = `"L"+"h"/"f"((9"N")/(10) - "c.f.")`
= `80 + (20)/(90)(216 - 135)`
= `80+2/9(81)`
= 80 + 18
∴ D9 = 98
P20 class = class containing `((20"N")/100)^"th"` observation
∴ `(20"N")/(100) = (20 xx 240)/(100)` = 48
Cumulative frequency which is just greater than (or equal to) 48 is 50.
∴ P20 lies in the class 40 – 60
∴ L = 40, f = 35, c.f. = 15, h = 20
P20 = `"L"+"h"/"f"((20"N")/(100) - "c.f.")`
= `40 + (20)/(35)(48 - 15)`
= `40 + (4)/(7)(33)`
= `40+132/7`
∴ P20 = 58.86
APPEARS IN
संबंधित प्रश्न
Calculate D6 and P85 for the following data:
79, 82, 36, 38, 51, 72, 68, 70, 64, 63.
The daily wages (in Rs.) of 15 laboures are as follows:
230, 400, 350, 200, 250, 380, 210, 225, 375, 180, 375, 450, 300, 350, 250
Calculate D8 and P90.
Calculate 2nd decide and 65th percentile for the following:
| x | 80 | 100 | 120 | 145 | 200 | 280 | 310 | 380 | 400 | 410 |
| f | 15 | 18 | 25 | 27 | 40 | 25 | 19 | 16 | 8 | 7 |
From the following data calculate the rent of 15th, 65th and 92nd house.
| House rent (in ₹) | 11000 | 12000 | 13000 | 15000 | 14000 | 16000 | 17000 | 18000 |
| No. of houses | 25 | 17 | 13 | 14 | 15 | 8 | 6 | 2 |
Weekly wages for a group of 100 persons are given below:
| Wages (in ₹) | 0 – 500 | 500 – 1000 | 1000 – 1500 | 1500 – 2000 | 2000 – 2500 |
| No. of persons | 7 | ? | 25 | 30 | ? |
D3 for this group is ₹ 1100 Calculate the missing frequencies.
In a particular factory, workers produce various types of output units.
The following distribution was obtained.
| Output units Produced | No. of workers |
| 70 – 74 | 40 |
| 75 – 79 | 45 |
| 80 – 84 | 50 |
| 85 – 89 | 60 |
| 90 – 94 | 70 |
| 95 – 99 | 80 |
| 100 – 104 | 100 |
Find the percentage of workers who have produced less than 82 output units.
The data gives number of accidents per day on a railway track. Compute Q2, P17, and D7.
4, 2, 3, 5, 6, 3, 4, 1, 2, 3, 2, 3, 4, 3, 2.
The distribution of daily sales of shoes (size-wise) for 100 days from a certain shop is:
| Size of shoes | 2 | 4 | 3 | 5 | 7 | 6 | 8 |
| No. of days | 14 | 20 | 13 | 19 | 13 | 13 | 8 |
Compute Q2, D1, and P95.
In the frequency distribution of families given below, the number of families corresponding to expenditure group 2000 - 4000 is missing from the table. However value of 25th percentile is 2880. Find the missing frequency.
| Weekly Expenditure (₹1000) | 0 – 2 | 2 – 4 | 4 – 6 | 6 – 8 | 8 – 10 |
| No. of families | 14 | ? | 39 | 7 | 15 |
Calculate Q1, D6, and P15 for the following data:
| Mid value | 25 | 75 | 125 | 175 | 225 | 275 |
| Frequency | 10 | 70 | 80 | 100 | 150 | 90 |
Daily income for a group of 100 workers are given below:
| Daily income (in₹) | 0 – 50 | 50 – 100 | 100 – 150 | 150 – 200 | 200 – 250 |
| No. of persons | 7 | ? | 25 | 30 | ? |
P30 for this group is ₹ 110. Calculate the missing frequencies.
The distribution of a sample of students appearing for a C.A. examination is:
| Marks | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 | 500 – 600 |
| No. of students | 130 | 150 | 190 | 220 | 280 | 130 |
Help C.A. institute to decide cut-off marks for qualifying an examination when 3% of students pass the examination.
Find Q1, D6, and P78 for the following data:
| C.I. | 8 – 8.95 | 9 – 9.95 | 10 – 10.95 | 11 – 11.95 | 12 – 12.95 |
| f | 5 | 10 | 20 | 10 | 5 |
