If the average of 5 numbers is 30, what is the sum of the 5 numbers?

Sum = average × count = 30 × 5 = 150. This is the basic rearrangement of the average formula: average = sum/count, therefore sum = average × count. This relationship is the key to many average problems. Variations: (1) 'Average of 4 numbers is 25; if one number is removed and the new average is 23, what was the removed number?' Original sum: 25 × 4 = 100; new sum: 23 × 3 = 69; removed number: 100 - 69 = 31. (2) 'A class of 30 has an average grade of 85; another class of 20 has an average of 75. What is the combined average?' Combined sum: (30 × 85) + (20 × 75) = 2,550 + 1,500 = 4,050; combined count: 50; combined average: 4,050/50 = 81. (3) Common ASVAB variations of these problems test understanding that you cannot simply average the averages when the groups have different sizes — you must use weighted averages or compute from sums.