Question

. Find the median and mean of the following frequency distribution
70-79
80-89
90-99
100-109
110 119
Weekly wages 60-69
(in Rs)
No. of days 5
15
20
20
Q35. A straight highway leads to the foot of a tower. A man standing at the top of the tower obsenes a
car at an angle of depression of 30°. Which is approaching the foot of the tower with a uniformed
speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by
the ar to reach the foot of the tower from this point.
Or
A boat goes 30 cm upstream and 44 km downstream in ten hours. In thirteen hours, it can go 40 km
upstream and 55 km downstream Determine the speed of the stream and that of the boat in stil
​

Answer 1

Answer:

Here, the frequency table is given in inclusive form. So we first transform it into exclusive form by subtracting and adding h/2 to the lower and upper limits respectively of each class, whereh denotes the difference of lower and upper limit of a class and the upper limit of the previous class.

Transforming the above table into exclusive form and preparing the cumulative frequency table, we get

Weekly wages (in Rs.) No. of workers Cumulative frequency

59.5- 69.5 5 5

69.5- 79.5 15 20

79.5- 89.5 20 40

89.5- 99.5 30 70

99.5- 109.5 20 90

109.5- 119.5 8 98

N=∑f

i

=98

We have,

N=98.∴N/2=49

The cumulative frequency just greater than N/2 is 70 and corrssponding class is 89.5−99.5,So,89.5−99.5 is the median class.

∴l=89.5,h=10,f=30,andF=40

Now, Median =l+

f

2

N

−f

×h

⇒Median=89.5+

30

49−40

×10=92.5