Simple tricks to calculate average of numbers

AVERAGE

  • An average or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by  n
  • Averages of a group is defined as the ratio of the sum of all the items in the group to the number of items in the group.
  • Average=(Number of items in the group )/(Sum of all items in the group)

​                 Now, the sum of all items can be the sum of a number of quantities like apple, people etc or sum of values of the item like 10 coins of 2Rs each etc’. 

  • Some Important Formulas :
  • Average =total of data  /  No. ofdata
  •   If the value of each item is increase by the same value a, then the average of the group or items will also increase by a.
  •  If the value of each item is decreased by the same value a, then the average of the group of items will also decrease by a.
  •  If the value of each item is multiplied by the same value a, then the average of the group or items will also get multiplied by a.
  •  If the value of each item is divided by the same value a, then the average of the group or items will also get divided by a.
  •  If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.
  • Average of n natural nos = (n+1​)/2
  • Average of even No’s(n+1)
  • Average of odd Nos = n
  • General Formula ={First number +Last number}/2

The average of 9 numbers is 40.The average of first 5 numbers is 30 and that of the last 3 numbers is 45.What is the 6th number

The average of marks of 18 students was calculated as 63.But it was later found that the marks of one student had been wrongly entered as 48 instead of 58 and of another 62 instead of 34.The correct average is

The average weight of 16 crewmen in a boat is increased by 1/4 ​​ kg when one of the crewmen whose weight is 53 kg is replaced by a new man. What is the weight of that new man (kg)

The mean of 20 items is 55.If two items 45 and 30 are removed, the new mean of the remaining items is

A cricketer has a certain average of runs for his 8 innings. In the ninth innings he scores 100 runs there by increases his average by 5 runs. What is the earlier average of runs is

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