The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table: Length (mm): 118-126  127-135  136-144  145-153  154-162  163-171  172-180 No. of leaves:         3         5          9         12        5          4         2. Find the mean length of leaf.

The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: (i) Draw a histogram to represent the given data.(ii) Is there any other suitable graphical representation for the same data?(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long?Why?

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is

Construct a frequency distribution table for the following data, taking class-intervals 4-6, 6-8 , ............. 14-16 . 11.5, 6.3, 7.8, 9.2, 10.5, 4.5, 6, 8.3, 12.5, 15.8, 7.4, 5.3, 8.4, 15.2, 8.9, 9.8, 8.25, 6.5, 5.8, 10.5, 14.2, 15.3, 11.7, 9.9, 8.8, 6.6, 4.3, 4.7, 9.4, 10.1, 15.5, 14.4, 12.2, 7.7, 5.5 .