Question

Q:- Fo||owing is the height of 10 students;
Student's: A B C D E F G H I J
Height (in CM's): 155, 153, 168, 160, 162, 166, 164, 180, 157, 165
Calculate arithmetic mean using Short cut method.

Class- XI
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Answer 1

Given :-

• No of students = 10

To Find :-

• The arithmetic mean of heights of students by using Short cut method.

Solution :-

• To calculate the arithmetic mean of heights of students at first we have to draw a table. then calculate the arithmetic mean by applying formula.

From here refer to the attachment :-

• By using formula of short cut method :-

⇒ Arithmetic mean = A + Σfd/Σf

• A denotes = Assume mean
• f denotes = frequency (heights of students)
• d denotes = deviation
• A = 162. Σfd = 2168. Σf = 1622

⇒ 162 + 2168/1622

⇒ 162 + 1.3

⇒ 163.3

⇒ 163cm (approx)

Hence,

• The arithmetic mean = 163cm

Answer 2

Given :-

Student's: A B C D E F G H I J

Height (in CM's): 155, 153, 168, 160, 162, 166, 164, 180, 157, 165

To Find :-

Arthimetic mean

Solution :-

Arthimetic mean - A + Σfd/Σf

Taking mean as 162 as it lies in the middle

$\left[\begin{array}{ccc}\bf Height&\bf Mean_{Difference}&\bf Product\\155&155-162=-7&155(-7)=-1085\\153&153-162=-9&153(-9)=-1377\\ 168&168-162=6&168(6)=1008\\ 160&160-162=-2&160(-2)=-320\\162&162-162=0&162(0)=0\\ 166&166-162=4&166(4)=664\\ 164&164-162=2&164(2)=328\\ 180&180-162=18& 180(18)=3240\\157&157-162=-5&157(-5)=-785\\ 165&165-162=3&165(3)=495\\\sf \sum f =1622&&\sf \sum fd=2168 \end{array}\right]$

By using the above formula

[Note - I'm writing A.M instead of the Arithmetic mean]

A.M = 162 + (2168/1622)

A.M = 162 + 1.33

A.M = 163.33 cm