Forty candidates from $10 t h$ class of a school appear for a test. The number of questions (out of $60$ ) attempted by them in forty five minutes is given here.
$52, 42, 40, 36, 12, 28, 15, 37, 35, 22, 39, 50, 54, 39, 21, 34, 46, 31, 10, 09$ ,
$13, 24, 29, 31, 49, 58, 40, 44, 37, 28, 13, 16, 29, 36, 39, 41, 47, 55, 52, 09$ .
Prepare a frequency distribution table with the class size $10$ and answer the following:
(i) Which class has the highest frequency?
(ii) Which class has the lowest frequency?
(iii) Write the upper and lower limits of the class $(20 - 29)$ .
(iv) Which two classes have the same frequency?

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Solution

Let us first prepare the frequency distribution table pertaining to this data.
Using this table, we can observe:
(i) $(30 - 39)$ has the highest frequency i.e. $11$ ;
(ii) $(0 - 9)$ has the lowest frequency i.e. $2$ ;
(iii) upper limit is $29.5$ and lower limit is $19.5$ of the class $(20 - 29)$ ;
(iv) $(10 - 19)$ and $(50 - 59)$ have the same frequency.

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40

100

75, 65, 57, 50, 32, 54, 75, 67, 75, 88, 80, 42, 40, 41, 34, 78, 43, 61, 42, 46

68, 52, 43, 49, 59, 49, 67, 34, 33, 87, 97, 47, 46, 54, 48, 45, 51, 47, 41, 43

10

(30 - 39), (40 - 49), . . .

30 - 39

The marks scored by 40 candidates in an examination (out of 100) is given below:

75, 65, 57, 50, 32, 54, 75, 67, 75, 88, 80, 42, 40, 41, 34, 78, 43, 61,

42, 46, 68, 52, 43, 49, 59, 49, 67, 34, 33, 87, 97, 47, 46, 54, 48, 45,

51, 47, 41, 43.

Prepare a frequency distribution table with the class size 10. Take the class intervals as (30 - 39), (40 - 49), … and answer the following question:

(a) Which class intervals have highest and lowest frequency?

(b) Write the upper and lower limits of the class interval 30-39.

The width of each of five continuous classes in a frequency distribution is 5 and the lower class - limit of the lowest class is 10.

Find the upper class - limit of the highest class.

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