Question

Gurpreet is very fond of doing research on plants. She collected some leaves from different plants and measured their lengths in mm.

The data obtained is represented in the following table:

Length (in mm):	70 - 80	80 - 90	90 - 100	100 - 110	110 - 120	120 - 130	130 - 140
Number of leaves:	3	5	9	12	5	4	2

Based on the above information, answer the following questions:

1. Write the median class of the data.    1
2. How many leaves are of length equal to or more than 10 cm?    1
3. 1. Find median of the data.    2
      OR
   2. Write the modal class and find the mode of the data.    2

Answer 1

For the given data we have,

Length (in mm):	Frequency (f)	Cumulative Frequency (Cf)
70 - 80	3	3
80 - 90	5	8
90 - 100	9	17
100 - 110	12	29
110 - 120	5	34
120 - 130	4	38
130 - 140	2	40

(i)

We have,

N = 40

`N/2 = 20`

So, median class is 100 - 110.

(ii)

We know that, 10 cm = 100 mm

Number of leaves greater than 100 mm

= 12 + 5 + 4 + 2 = 23

(iii) (a)

Median class is 100 - 110

So, I = 100

⇒ f = 12, Cf = 17

⇒ h = 10

Median = `l + ((N/2 - Cf))/f xx h`

Median = 100 + `((20 - 17))/12 xx 10`

Median = 100 + 2.5

Median = 102.5

OR (b)

We have,

Modal class as 100 - 110

So, I = 100

⇒ f₁ = 12, f₀ = 9, f₂ = 5

⇒ h = 10

We know that,

Mode = `l + (f_1 - f_0)/(2f_1 - f_0 - f_2) xx h`

Mode = `100 + (12 - 9)/(24 - 9 - 5) xx 10`

Mode = 100 + 3

Mode = 103