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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
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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
800 people were asked whether they wear glasses for reading with the following results.
| Age | Wear glasses | Do not wear glasses |
| ≤ 30 | 310 | 90 |
| > 30 | 290 | 110 |
Compute the X2 square statistic.
Concept: undefined >> undefined
Out of a sample of 120 persons in a village, 80 were administered a new drug for preventing influenza and out of them 18 were attacked by influenza. Out of those who were not administered the new drug, 10 persons were not attacked by influenza: Prepare to compute the χ2 square statistic.
Concept: undefined >> undefined
A box contains 11 tickets numbered from 1 to 11. Two tickets are drawn at random with replacement. If the sum is even, find the probability that both the numbers are odd.
Concept: undefined >> undefined
