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Consider the ...

Question

Consider the following marks (out of $50$ ) scored in mathematics by $50$ students of $8 t h$ class:
$41, 31, 33, 32, 28, 31, 21, 10, 30, 22, 33, 37, 12, 05, 08, 15, 39, 26, 41, 46, 34, 22, 09$ .
$11, 16, 22, 25, 29, 31, 39, 23, 31, 21, 45, 47, 30, 22, 17, 36, 18, 20, 22, 44, 16, 24, 10, 27, 39, 28, 17$ .
Prepare a frequency distribution table

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Solution

If we prepare a frequency distribution table for each observation, then the table would be too long. So for convenience, we make groups of observations like $0 - 9, 10 - 19$ and so on. We obtain a frequency of distribution of the number of observations coming under each group. In this way, we prepare a frequency distribution table for the above data as below:

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Q. The marks scored by 40 students of class IX in mathematics are given below:
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54

Prepare a frequency distribution with class size of 10 marks.

There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.

70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47

By taking classes 30-40, 40-50, .... prepare the less than type cumulative frequency table

Using the table, answer the following questions :

(i) How many students, have scored marks less than 80 ?

(ii) How many students have scored marks less than 40 ?

(iii) How many students have scored marks less than 60 ?

Prepare a frequency table of the following scores obtained by 50 students in a test:

42, 51, 21, 42, 37, 37, 42, 49, 38, 52, 7, 33, 17,

44, 39, 7, 14, 27, 39, 42, 42, 62, 37, 39, 67, 51,

53, 53, 59, 41, 29, 38, 27, 31, 54, 19, 53, 51, 22,

61, 42, 39, 59, 47, 33, 34, 16, 37, 57, 43

Q. Prepare a frequency table of the following scores obtained by 50 students in a test:

42	51	21	42	37	37	42	49	38	52
7	33	17	44	39	7	14	27	39	42
42	62	37	39	67	51	53	53	59	41
29	38	27	31	54	19	53	51	22	61
42	39	59	47	33	34	16	37	57	43

The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.

55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.

From the prepared table, answer the following questions :

(i) How many students obtained marks 40 or above 40 ?

(ii) How many students obtained marks 90 or above 90 ?

(iii) How many students obtained marks 60 or above 60 ?

(iv) What is the cumulative frequency of equal to or more than type of the class 0-10?

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