Find the arithmetic mean of the below case

Monthly wage	Number of workers
700	2
800	8
900	8
1000	2

Explanation:

Concept:

Arithmetic Mean:

• The arithmetic mean is the sum of a collection of numbers divided by the count of numbers in the collection.
• Given a data set X = {x₁, x₂, x₃, .... x_n}, the arithmetic mean is denoted by \(\bar{x}\) .

           \(\bar{x} = \frac{1}{n}\times \sum_{i=1}^{n}x_i\)

• For calculating the mean when the frequency of the observations is given, such that x1, x2, x3, … xn is the recorded observations, and f1, f2, f3 … fn is the respective frequencies of the observations then

​           \(\bar{x} = \frac{\sum_{i=1}^{n}f_ix_i} {\sum_{i=1}^{n}f_i}\)

Calculation:

Data given, we take monthly wage as dataset and number of workers as frequency data points,

x₁ = 700, f₁ = 2

x₂ = 800, f₂ = 8

x₃ = 900, f₃ = 8

x₄ = 1000, f₄ = 2

\(\bar{x} = \frac{(700\times2+800\times8+900\times8+1000\times2)} {(2+8+8+2)}\)

∴ \(\bar{x} = \frac{17000}{20} = 850\)