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Find the area of triangles whose vertices are A(−1, 2), B(2, 4), C(0, 0).
Concept: undefined >> undefined
Express the following recurring decimal as a rational number.
`3.4bar(56)`
Concept: undefined >> undefined
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The following table gives frequency distribution of marks of 100 students in an examination.
| Marks | 15 –20 | 20 – 25 | 25 – 30 | 30 –35 | 35 – 40 | 40 – 45 | 45 – 50 |
| No. of students | 9 | 12 | 23 | 31 | 10 | 8 | 7 |
Determine D6, Q1, and P85 graphically.
Concept: undefined >> undefined
The following table gives the distribution of daily wages of 500 families in a certain city.
| Daily wages | No. of families |
| Below 100 | 50 |
| 100 – 200 | 150 |
| 200 – 300 | 180 |
| 300 – 400 | 50 |
| 400 – 500 | 40 |
| 500 – 600 | 20 |
| 600 above | 10 |
Draw a ‘less than’ ogive for the above data. Determine the median income and obtain the limits of income of central 50% of the families.
Concept: undefined >> undefined
The following frequency distribution shows the profit (in ₹) of shops in a particular area of city:
| Profit per shop (in ‘000) | No. of shops |
| 0 – 10 | 12 |
| 10 – 20 | 18 |
| 20 – 30 | 27 |
| 30 – 40 | 20 |
| 40 – 50 | 17 |
| 50 – 60 | 6 |
Find graphically The limits of middle 40% shops.
Concept: undefined >> undefined
The following frequency distribution shows the profit (in ₹) of shops in a particular area of city:
| Profit per shop (in ‘000) | No. of shops |
| 0 – 10 | 12 |
| 10 – 20 | 18 |
| 20 – 30 | 27 |
| 30 – 40 | 20 |
| 40 – 50 | 17 |
| 50 – 60 | 6 |
Find graphically the number of shops having profile less than 35,000 rupees.
Concept: undefined >> undefined
The following is the frequency distribution of overtime (per week) performed by various workers from a certain company.
Determine the values of D2, Q2, and P61 graphically.
| Overtime (in hours) |
Below 8 | 8 – 12 | 12 – 16 | 16 – 20 | 20 – 24 | 24 and above |
| No. of workers | 4 | 8 | 16 | 18 | 20 | 14 |
Concept: undefined >> undefined
Draw ogive for the following data and hence find the values of D1, Q1, P40.
| Marks less than | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |
| No. of students | 4 | 6 | 24 | 46 | 67 | 86 | 96 | 99 | 100 |
Concept: undefined >> undefined
The following table shows the age distribution of head of the families in a certain country. Determine the third, fifth and eighth decile of the distribution graphically.
| Age of head of family (in years) |
Numbers (million) |
| Under 35 | 46 |
| 35 – 45 | 85 |
| 45 – 55 | 64 |
| 55 – 65 | 75 |
| 65 – 75 | 90 |
| 75 and Above | 40 |
Concept: undefined >> undefined
The following table gives the distribution of females in an Indian village. Determine the median age of graphically.
| Age group | No. of females (in ‘000) |
| 0 – 10 | 175 |
| 10 – 20 | 100 |
| 20 – 30 | 68 |
| 30 – 40 | 48 |
| 40 – 50 | 25 |
| 50 – 60 | 50 |
| 60 – 70 | 23 |
| 70 – 80 | 8 |
| 80 – 90 | 2 |
| 90 – 100 | 1 |
Concept: undefined >> undefined
Draw ogive for the Following distribution and hence find graphically the limits of weight of middle 50% fishes.
| Weight of fishes (in gms) | 800 – 890 | 900 – 990 | 1000 – 1090 | 1100 – 1190 | 1200 – 1290 | 1300 –1390 | 1400 – 1490 |
| No. of fishes | 8 | 16 | 20 | 25 | 40 | 6 | 5 |
Concept: undefined >> undefined
Find graphically the values of D3 and P65 for the data given below:
| I.Q of students | 60 – 69 | 70 – 79 | 80 – 89 | 90 – 99 | 100 – 109 | 110 – 119 | 120 – 129 |
| No. of students | 20 | 40 | 50 | 50 | 20 | 10 | 10 |
Concept: undefined >> undefined
For a data set, sum of upper and lower quartiles is 100, difference between upper and lower quartiles is 40 and median is 50. Find the coefficient of skewness.
Concept: undefined >> undefined
For a data set with upper quartile equal to 55 and median equal to 42. If the distribution is symmetric, find the value of lower quartile.
Concept: undefined >> undefined
Obtain the coefficient of skewness by formula and comment on nature of the distribution.
| Height in inches | No. of females |
| Less than 60 | 10 |
| 60 – 64 | 20 |
| 64 – 68 | 40 |
| 68 – 72 | 10 |
| 72 – 76 | 2 |
Concept: undefined >> undefined
Calculate Skb for the following set of observations of yield of wheat in kg from 13 plots:
4.6, 3.5, 4.8, 5.1, 4.7, 5.5, 4.7, 3.6, 3.5, 4.2, 3.5, 3.6, 5.2
Concept: undefined >> undefined
For a frequency distribution Q3 – Q2 = 90 And Q2 – Q1 = 120, find Skb.
Concept: undefined >> undefined
Following table shows the classification of applications for secretarial and for sales positions according to gender. Calculate the value of χ2 Statistic.
|
Offered |
Denied | |
| Male | 75 | 150 |
| Female | 25 | 50 |
Concept: undefined >> undefined
200 teenagers were asked which take-out food do they prefer - French fries, burger, or pizza. The results were -
| French fries | Burger | Pizza | |
| Boys | 6 | 20 | 24 |
| Girls | 18 | 40 | 92 |
Compute χ2 Statistics.
Concept: undefined >> undefined
A sample of men and women who had passed their driving test either in 1st attempt or in 2nd attempt surveyed. Compute χ2 statistics.
| Passed in → |
First attempt | Second attempt |
| Men | 32 | 28 |
| Women | 8 | 12 |
Concept: undefined >> undefined
