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.