Advertisements
Advertisements
Question
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.
Solution
To decide cut off marks for qualifying an examination when 3% of students pass, we have to find P97.
We construct the less than cumulative frequency table as given below:
| Marks | No. of students (f) |
Less than cumulative frequency (c.f.) |
| 0 – 100 | 130 | 130 |
| 100 – 200 | 150 | 280 |
| 200 – 300 | 190 | 470 |
| 300 – 400 | 220 | 690 |
| 400 – 500 | 280 | 970 |
| 500 – 600 | 130 | 1100 ← P97 |
| Total | 1100 |
Here, N = 1100
P97 class = class containing `((97"N")/100)^"th"` observation
∴ `(97"N")/100=(97×1100)/100` = 1067
Cumulative frequency which is just greater than (or equal) to 1067 is 1100.
∴ P97 lies in the class 500 – 600
∴ L = 500, h = 100, f = 130, c.f. = 970
∴ P97 = `"L" + "h"/"f" ((97"N")/100 - "c.f.")`
= `500 + 100/130 (1067 - 970)`
= `500 + 10/13 (97)`
= 500 + 74.62
= 574.62 ≈ 575
∴ The cut-off marks for qualifying an examination is 575.
APPEARS IN
RELATED QUESTIONS
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.
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 |
The following frequency distribution shows the weight of students in a class:
| Weight (in Kg) | 40 | 45 | 50 | 55 | 60 | 65 |
| Number of Students | 15 | 40 | 29 | 21 | 10 | 5 |
(a) Find the percentage of students whose weight is more than 50 kg.
(b) If the weight column provided is of mid values then find the percentage of students whose weight is more than 50 kg.
Calculate D4 and P48 from the following data:
| Mid value | 2.5 | 7.5 | 12.5 | 17.5 | 22.55 | Total |
| Frequency | 7 | 18 | 25 | 30 | 20 | 100 |
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 |
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.
The weekly profit (in rupees) of 100 shops are distributed as follows:
| Profit per shop | No. of shops |
| 0 – 1000 | 10 |
| 1000 – 2000 | 16 |
| 2000 – 3000 | 26 |
| 3000 – 4000 | 20 |
| 4000 – 5000 | 20 |
| 5000 – 6000 | 5 |
| 6000 – 7000 | 3 |
Find the limits of the profit of middle 60% of the shops.
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.
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 |
