Mean Of A Set Of Numbers
The collection, classification, tabulation, and graphical representation of data compress the size of the original data and make it understandable
. Sometimes, as comparisons are not possible by means of graphical representation alone, a need was felt to represent the data arithmetically in the form of a number which represents certain features of the entire data. One such measure of central value is known as average. In general, the arithmetic mean is also known as mean or average.
Introduction to mean of a set of numbers:
The arithmetic mean of a set of numbers is defined as the sum of the given numbers divided by the number of values.
Let the numbers in the given set be x1, x2, x3 xn.
Number of data in the given set is n
'barx' = Arithmetic mean.
'barx = (sum x_i)/n'
'sum_(i=1)^n x_i = x_1 + x_2 + x_3+... + x_n'
'barx = (x_1 + x_2+x_3+... + x_n)/n'
Let us see some examples on mean.
Problems on Finding Mean of a Set of Numbers:
Ex 1: The scores made by a cricketer in 10 innings are given. Find the mean score
45, 70, 60, 0, 20, 18, 100, 90, 11, 0
Sol:
Step 1: Number of data, n = 10
Step 2: Find 'sum_(i=1)^10'
'sum_(i=1)^10 x_i = 45+70+60+0+20+18+100+90+11+0 = 414'
Step 3: Write the arithmetic mean formula
'barx = (sum x_i)/n'
Step 4: Plug the values
'barx = 414/10 = 41.4'
Step 5: Write the solution
The mean score = 41.4
Ex 2: Find the value of y if the mean of 5, y+3, y + 2, 10, 12 and 14 is 9
Sol:
Step 1: Write the given details
mean = 9
n = 6
Step 2: Find the sum of the given values
'sum x_i = 5 + y + 2 + y + 3 + 10+12 + 14 = 46 + 2y'
Step 3: Write the arithmetic mean formula
'barx = (sum x_i)/n = (46+2y)/6 = 9'
Step 4: Solve for y
46 + 2y = 54
2y = 54 - 46 = 8
y = 4
Step 5: Write the solution
y = 4
Problems for Practice Based on Mean:
Find the arithmetic mean of the marks obtained by 8 pupils in a certain examination
18, 20, 40, 34, 62, 70, 50, 12
Ans: 38.25
The mean of the values of 4, 8, 7, 1, x is 5. Find the value of x.
Ans: 5
by: Omkar Nayak
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