Answer

Here we have, cumulative frequency distribution less than type. First we convert it into an ordinary frequency distribution. We observe that the number of students getting marks less than 10 is 5 and 9 students have secured marks less than 20. Therefore,  number of students getting marks between 10 and 20 ( inclusive 0 and exclusive 10) is 9−5=4. Similarly, the number of students getting marks between 20 and 30 is 17−9=8 and so on. Thus, we have the following distribution frequency distributionAnswer:

Step-by-step explanation:Marks:  0−10  10−20  20−30   30−40  40−50  50−60  60−70  70−80  80−90  90−100

Number of students:   5     4      8       12       16      15     10       8       5       2

Let US Let us now compute arithmetic mean by taking 55 and the assumed mean.

Computation of Mean

Marks Mid-value Frequency ui​10xi​−55​ fi​ui​

0−10  5 5 −5 −25

10−20  10 4 −4 −16

20−30   25 8 −3 −24

30−40  35 12 −2 −24

40−50  45 16 −1 −16

50−60  55 15  0 0

60−70  65 10  1 10

70−80  75 8  2 16

80−90  85 5  3 15

90−100  95 2  4 8

Total   N=∑fi​=85  ∑fi​ui​=−56

We have,

N=N=∑fi​=85,∑fi​ui​=−56,h=10andA=55

∴X=A+h(N1​∑fi​ui​)

⇒X=55+10×85−56​=55−6.59=48.41Marks.

Hence, mean marks scored by the students = 48.41.