The average of seven consecutive positive integers is 259. If the next five odd numbers are included, then what is the average of all the numbers (correct to two decimal places)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 262.33.
Formula used:
Average = Sum of observation/number of observation ----- (1)
Calculations:
Let the 7 consecutive numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6 and
next consecutive numbers are x + 7, x + 9, x + 11, x + 13, x + 15
Sum of first 7 numbers = 7x + 21
Using equation (1)
⇒ 7x + 21 = 259 × 7
⇒ x + 3 = 259
⇒ x = 256
Sum of all numbers = 12a + 76
Required average = (12a + 76)/12
⇒ a + 6.33 = 256 + 6.33 = 262.33