Advertisements
Advertisements
Question
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.
Solution
To draw a ogive curve, we construct the less than cumulative frequency table as given below:
| Daily wages | No. of families (f) |
Less than cumulative frequency (c.f.) |
| Below 100 | 50 | 50 |
| 100 – 200 | 150 | 200 |
| 200 – 300 | 180 | 380 |
| 300 – 400 | 50 | 430 |
| 400 – 500 | 40 | 470 |
| 500 – 600 | 20 | 490 |
| 600 above | 10 | 500 |
| Total | 500 |
The points to be plotted for less than ogive are (100, 50), (200, 200), (300, 380), (400, 430), (500, 470), (600, 490) and (700, 500).
Here, N = 500
For Q1, `"N"/4 = 500/4 = 125`
For Q2, `"N"/2=500/2 = 250`
For Q3, `"3N"/4=(3xx500)/4 = 375`
∴ We take the points having Y coordinates 125, 250, and 375 on Y-axis. From these points, we draw lines parallel to X-axis. From the points where these lines intersect the curve, we draw perpendiculars on X-axis. X-Co-ordinates of these points gives the values of Q1, Q2, and Q3.
∴ Q1 ≈ 150, Q2 ≈ 228, Q3 ≈ 297
∴ Median = 228
50% of families lies between Q1 and Q3
∴ Limits of income of central 50% of families are from ₹ 150 to ₹ 297.
APPEARS IN
RELATED QUESTIONS
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.
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.
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.
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 |
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 |
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 |
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 |
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 |
Determine graphically the value of median, D3, and P35 for the data given below:
| Class | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 | 40 – 45 |
| Frequency | 8 | 14 | 8 | 25 | 15 | 14 | 6 |
The I.Q. test of 500 students of a college is as follows:
| I.Q. | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| Number of students | 41 | 52 | 64 | 180 | 67 | 45 | 40 | 11 |
Find graphically the number of students whose I.Q. is more than 55 graphically.
Draw an ogive for the following distribution. Determine the median graphically and verify your result by mathematical formula.
| Height (in cms.) | No. of students |
| 145 − 150 | 2 |
| 150 − 155 | 5 |
| 155 − 160 | 9 |
| 160 − 165 | 15 |
| 165 − 170 | 16 |
| 170 − 175 | 7 |
| 175 − 180 | 5 |
| 180 − 185 | 1 |
Draw a cumulative frequency curve more than type for the following data and hence locate Q1 and Q3. Also, find the number of workers with daily wages
(i) Between ₹ 170 and ₹ 260
(ii) less than ₹ 260
| Daily wages more than (₹) | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 |
| No. of workers | 200 | 188 | 160 | 124 | 74 | 49 | 31 | 15 | 5 |
Draw ogive of both the types for the following frequency distribution and hence find median.
| Marks | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| No. of students | 5 | 5 | 8 | 12 | 16 | 15 | 10 | 8 | 5 | 2 |
