Correct Answer - Option 4 : increase by 1
Given:
Average of 5 consecutive numbers = n
Formula used:
Average = Sum of observations/No of observations
Calculation:
Let the first number be = a
⇒ Second number = a + 1
⇒ Third number = a + 2
⇒ Fourth number = a + 3
⇒ Fifth number = a + 4
Average of 5 consecutive numbers = [a + (a + 1) + (a + 2) + (a + 3) + (a + 4)]/5
⇒ (5a + 10)/5 = n
⇒ 5n = 5a + 10
⇒ n = a + 2
⇒ a = n - 2 (1)
After adding 2 more consecutive numbers;
⇒ Sixth number = a + 5
⇒ Seventh number = a + 6
New Average = [(5a + 10) + (a + 5) + (a + 6)]/7
⇒ (7a + 21)/7
⇒ a + 3
By putting the value of 'a' in equation (1)
⇒ n - 2 + 3
⇒ n + 1
Changed average = (n + 1) - n = 1
∴ The average of 7 numbers will be increased by 1.
