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Show that `(-1 + sqrt3i)^3` is a real number.
Concept: undefined >> undefined
Calculate D6 and P85 for the following data:
79, 82, 36, 38, 51, 72, 68, 70, 64, 63.
Concept: undefined >> undefined
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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.
Concept: undefined >> undefined
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 |
Concept: undefined >> undefined
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 |
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
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 |
Concept: undefined >> undefined
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 |
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 2, 4, 6, 8, 10.
(Given: `sqrt8` = 2.8284)
Concept: undefined >> undefined
Find the coefficient of Variation of a sample which has mean equal to 25 and standard deviation of 5.
Concept: undefined >> undefined
A group of 65 students of class XI have their average height is 150.4 cm with coefficient of variation 2.5%. What is the standard deviation of their height?
Concept: undefined >> undefined
Two workers on the same job show the following results:
|
Worker P |
Worker Q | |
| Mean time for completing the job (hours) | 33 | 21 |
| Standard Deviation (hours) | 9 | 7 |
Regarding the time required to complete the job, which worker is more consistent?
Concept: undefined >> undefined
Two workers on the same job show the following results:
| Worker P | Worker Q | |
| Mean time for completing the job (hours) | 33 | 21 |
| Standard Deviation (hours) | 9 | 7 |
Which worker seems to be faster in completing the job?
Concept: undefined >> undefined
A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively. Which department has a larger bill?
Concept: undefined >> undefined
A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively. Which department has a larger variability in wages?
Concept: undefined >> undefined
The following table gives weights of the students of class A. Calculate the Coefficient of variation. `("Given": sqrt0.8 = 0.8944)`
| Weight (in kg) | Class A |
| 25 – 35 | 8 |
| 35 – 45 | 4 |
| 45 – 55 | 8 |
Concept: undefined >> undefined
Compute coefficient of variation for team A and team B.
| No. of goals | 0 | 1 | 2 | 3 | 4 |
| No. of matches played by team A | 19 | 6 | 5 | 16 | 14 |
| No. of matches played by team B | 16 | 16 | 5 | 18 | 15 |
Which team is more consistent?
Concept: undefined >> undefined
