# The arithmetic mean of the heights of the 3 members of a family is 135 cm. If a new member of height 119 cm comes, then what is the new arithmetic mea

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The arithmetic mean of the heights of the 3 members of a family is 135 cm. If a new member of height 119 cm comes, then what is the new arithmetic mean of heights of all the members of the family?
1. 131 cm
2. 135 cm
3. 127 cm
4. 129 cm

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Correct Answer - Option 1 : 131 cm

Given:

Arithmetic mean of family's height = 135 cm

Number of members = 3

Height of new member = 119 cm

Formula Used:

Arithmetic mean = Sum of heights/Number of members

Calculations:

Number of members = 3

Arithmetic mean = Sum of heights/Number of members

⇒ 135 = Sum of heights/3

⇒ 135 × 3 = Sum of heights

⇒ Sum of heights = 405 cm

Height of new member = 119 cm

Sum of heights of all members = 405 cm + 119 cm

⇒ Sum of heights of all members = 524 cm

Number of members = 3 + 1 = 4

Arithmetic mean of heights = 524/4

⇒

Arithmetic mean of heights = 131 cm

∴ The new arithmetic mean of heights of all the members of the family is 131 cm.