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Standard IX

Mathematics

Mathematical Expression for Mean

A class has 2...

Question

A class has 20 students whose ages (in years) are as follows. 14, 13, 14, 15, 12, 13, 13, 14, 15, 12, 15, 14, 12, 16, 13, 14, 14, 15, 16, and 12. Find the mean age of these students.
(3 marks)

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Solution

Age (in years) $x_{i}$ Number of students $f_{i}$ $f_{i}$ $x_{i}$

12 4 48

13 4 52

14 6 84

15 4 60

16 2 32

Total $\sum f_{i} =$ 20 $\sum f_{i} x_{i} =$ 276

(2 marks)
Mean = µ or $x$ = Σ $f_{i} x_{i}$ /Σ $f_{i}$ = 276/20=13.8

(1 mark)

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Draw frequency distribution table and bar graph for the following data :

Ages(in years) of students in a class:

$14, 13, 12, 13, 14, 15, 13, 14, 16, 15, 14, 13, 12, 12, 12, 13, 13, 13, 13, 15, 14, 14, 13, 13, 12, 12, 12, 15, 14, 12, 12, 13, 13, 14, 12, 16,$

$16, 13, 13, 12, 14, 14$

The following are the ages ( in years) of 25 students of a class.

Prepare a table using tally marks and then draw a pictograph using 1 for 2 students.

$15, 13, 16, 12, 14, 15, 16, 13, 12, 14, 16, 16, 15, 12, 11, 15, 16, 13, 12, 14, 15, 15, 12, 11, 16$

The marks of

20

students in a test were as follows:

5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20.

The mean is

Q. The marks (out of 25) obtained by students of a certain class are 11, 12, 14, 13, 17, 11, 12, 12, 17, 21, 24, 14, 11, 13, 12, 17, 21, 19, 19, 24, 14, 15, 12, 17, 15, 19, 21, 13, 16, and 15.
What is the mode of marks obtained by students of the class?

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Age (in years) $x_{i}$	Number of students $f_{i}$	$f_{i}$ $x_{i}$
12	4	48
13	4	52
14	6	84
15	4	60
16	2	32
Total	$\sum f_{i} =$ 20	$\sum f_{i} x_{i} =$ 276

A class has 20 students whose ages (in years) are as follows. 14, 13, 14, 15, 12, 13, 13, 14, 15, 12, 15, 14, 12, 16, 13, 14, 14, 15, 16, and 12. Find the mean age of these students. (3 marks)

Age (in years) xi Number of students fi fixi 12 4 48 13 4 52 14 6 84 15 4 60 16 2 32 Total ∑fi = 20 ∑fixi = 276 (2 marks) Mean = µ or x= Σfixi/Σfi= 276/20=13.8 (1 mark)

A class has 20 students whose ages (in years) are as follows. 14, 13, 14, 15, 12, 13, 13, 14, 15, 12, 15, 14, 12, 16, 13, 14, 14, 15, 16, and 12. Find the mean age of these students.
(3 marks)

Age (in years) $x_{i}$ Number of students $f_{i}$ $f_{i}$ $x_{i}$

12 4 48

13 4 52

14 6 84

15 4 60

16 2 32

Total $\sum f_{i} =$ 20 $\sum f_{i} x_{i} =$ 276

(2 marks)
Mean = µ or $x$ = Σ $f_{i} x_{i}$ /Σ $f_{i}$ = 276/20=13.8

(1 mark)