Class 10 Mathematics
1. The following distribution gives the daily income of 50 workers of a factory.
|Daily income (in Rs)||100-120||120-140||140-160||160-180||180-200|
|Number of workers||12||14||8||6||10|
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
|Daily income||Cumulative frequency|
|Less than 120||12|
|Less than 140||26|
|Less than 160||34|
|Less than 180||40|
|Less than 200||50|
2. During the medical checkup of 35 students of a class, their weights were recorded as follows:
|Weight (in kg)||Number of students|
|Less than 38||0|
|Less than 40||3|
|Less than 42||5|
|Less than 44||9|
|Less than 46||14|
|Less than 48||28|
|Less than 50||32|
|Less than 52||35|
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
|Weight (in kg)||Frequency||Cumulative Frequency|
Since `N = 35` and `n/2 = 17.5` hence median class = Less than 46-48
Here; `l = 46`, `cf = 14`, `f = 14` and `h = 2`
Median can be calculated as follows:
This value of median verifies the median shown in ogive.
3. The following table gives production yield per hectare of wheat of 100 farms of a village.
|Production yield (in kg)||50-55||55-60||60-65||65-70||70-75||75-80|
|Number of farms||2||8||12||24||38||16|
Change this distribution to a more than type distribution, and draw its ogive.
|Production yield||Cumulative frequency|
|More than 50||100|
|More than 55||98|
|More than 60||90|
|More than 65||78|
|More than 70||54|
|More than 75||16|