Sample Mean Formula

A sample is a subset of a bigger population of data. The sample mean formula is used to get the average value of a set of sample data. It is defined as the average of the sample’s measurements. If the sample is chosen at random, the sample mean may be used to calculate the population mean. It represents the assessment of the data’s centre and is used to determine the mean of any population.

Sample Mean Formula

The sample mean for a data set is defined as the sum of all the terms divided by the total number of terms. It is denoted by the symbol x̄.

x̄ = Σx_i / n

where,

 Σx_i is the sum of terms in the sample,

n is the number of terms in the sample.

Sample Problems

Problem 1. Find the sample mean of the data 15, 20, 72, 43, and 21.

Solution:

We have the sample, 15, 20, 72, 43, 21

Sum of terms(S) = 15 + 20+ 72 + 43 + 21 = 171

Number of terms(n) = 5

Using the formula for sample mean, we get

x̄ = S/n

= 171/5

= 34.2

Problem 2. Find the sample mean of the data 13, 31, 27, 72, 16, and 67.

Solution:

We have the sample, 13, 31, 27, 72, 16, 67

Sum of terms(S) = 13 + 31+ 27 + 72 + 16 + 67 = 171

Number of terms(n) = 6

Using the formula for sample mean, we get

x̄ = S/n

= 226/6

= 37.66

Problem 3. Find the sample mean of the data 42, 53, 92, 31, 56, 110, and 63.

Solution:

We have the sample, 42, 53, 92, 31, 56, 110, 63

Sum of terms(S) = 42 + 53+ 92 + 31 + 56 + 110 + 63 = 447

Number of terms(n) = 7

Using the formula for sample mean, we get

x̄ = S/n

= 447/7

= 63.85

Problem 4. Find the number of terms in the sample if their sum and mean are 132 and 22 respectively.

Solution:

We have, S = 132, x̄ = 22

Using the formula for sample mean, we get

x̄ = S/n

=> 22 = 132/n

=> n = 132/22

=> n = 6

Problem 5. Find the number of terms in the sample if their sum and mean are 315 and 35 respectively.

Solution:

We have, S = 315, x̄ = 35

Using the formula for sample mean, we get

x̄ = S/n

=> 35 = 315/n

=> n = 315/35

=> n = 9

Problem 6. In a class of 10 students, the data for marks of all the students is 20, 25, 30, 35, 40, 45, 50, 55, 60, 65. Find the average marks for the class.

Solution:

We have the sample, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65

Sum of terms(S) = 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 = 425

Number of terms(n) = 10

Using the formula for sample mean, we get

x̄ = S/n

= 425/10

= 42.5

Problem 7. Seven workers worked at a construction site for 15, 30, 45, 60, 75, 90, and 105 days respectively. Find the average number of days they worked.

Solution:

We have the sample, 15, 30, 45, 60, 75, 90, 105

Sum of terms(S) = 15 + 30 + 45 + 60 + 75 + 90 + 105 = 420 

Number of terms(n) = 7

Using the formula for sample mean, we get

x̄ = S/n

= 420/7

= 60