Question

7. From the following table, estimate the
number of students who obtained marks
between 40 and 45. (5 marks)
Marks
No of
Students
30-40 40-50 50-60 60-70 70-80
31 42 51 35 31​

Answer 1

Answer:

3 is the answer.

Step-by-step explanation:

There us no one else than 42,40 and 40 which lies in 40-45

Answer 2

Given

Marks :                 30-40  40-50 50-60 60-70 70-80

No of Students:    31           42      51      35       31​

To find

The number of students who obtained marks between 40 and 45.

Solution

The Newton’s Forward Difference Formula is given as,

⇒f(a+hu)=f(a)+uΔ(fa)+$\frac{u(u-1)}{2}$Δ²f(a)+...+$\frac{u(u-1)...(u-n+1)}{n}$Δⁿ(fa)

Now, we generate a forward difference table to find the maximum value i.e f(45),

x:         40  50    60      70     80

y=f(x):  31    73    124    159    190

Δf(a) :         42     51       35      31

Δ²f(a):                   9      -16       -4

Δ³f(a):                            -25      12

Δ⁴f(a):                                       37

Here, the first term (a) = 40 and the interval (h)= 10

∵ a+hu= 45

⇒u=0.5

Now, using the Newton’s Forward Difference Formula, we get

f(45)= 48

∴ number of students with marks < 45 = 48

From the above table,

number of students getting marks < 40 = 31

∴ number of students who obtained marks between 40 and 45

⇒48-31

⇒17

Hence, the number of students who obtained marks between 40 and 45 is 17