# Arithmetic Mean - Raw Data

#### definition

Arithmetic Mean: The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.

"Mean" = "Sum of all observations"/"number of observations".

# Arithmetic Mean:

• Arithmetic mean is one of the representative values of data.
• The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.

• It is denoted by the symbol x, read as bar x.

• The average or Arithmetic Mean (A.M.) or simply mean is defined as follows:
"Mean" = "Sum of all observations"/"number of observations"

#### Example

Two vessels contain 20 liters and 60 liters of milk respectively. What is the amount that each vessel would have if both share the milk equally?

The average or the arithmetic mean would be

= "Total quantity of milk"/"Number of vessels"

= (20 + 60)/2 litres

= 40 litres.

Thus, each vessel would have 40 liters of milk.

#### Example

Ashish studies for 4 hours, 5 hours, and 3 hours respectively on three consecutive days. How many hours does he study daily on average?

The average study time of Ashish would be

"Total number of study hours"/"Number of days for which he studied" = (4 + 5 + 3)/3 hours = 4 hours per day

Thus, we can say that Ashish studies for 4 hours daily on an average.

#### Example

A batsman scored the following number of runs in six innings: 36, 35, 50, 46, 60, 55. Calculate the mean runs scored by him in an inning.

Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282.

To find the mean, we find the sum of all the observations and divide it by the number of observations.

Therefore, in this case, mean = 282/6 = 47.

Thus, the mean runs scored in an inning is 47.

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