Question

A student was asked to find the arithmetic mean of the following 12 numbers : 3, 10, 8, 9, 13, 13, 10, 20, 16, 21, 14 and x He found the mean to be 12. The value of x will be

• A. 9
• B. 7
• C. 14
• D. 12

Answer 1

Answer:

B. 7

Understanding Arithmetic Mean (Average)

• The Arithmetic Mean, often simply called the average, is a fundamental concept in statistics and a very common topic in competitive exams.

• It is calculated by summing all the values in a dataset and then dividing by the total number of values.

• The formula is: Mean = (Sum of all observations) / (Number of observations).

Solving the Problem

• We are given 12 numbers: 3, 10, 8, 9, 13, 13, 10, 20, 16, 21, 14, and an unknown 'x'.

• The total number of observations (n) is 12.

• The given arithmetic mean is 12.

• First, calculate the sum of the known 11 numbers:

  • 3 + 10 + 8 + 9 + 13 + 13 + 10 + 20 + 16 + 21 + 14 = 137.

• Now, include the unknown 'x' in the sum: The total sum of all 12 observations is (137 + x).

• Apply the arithmetic mean formula:

  (137 + x) / 12 = 12

• To find 'x', multiply both sides of the equation by 12:

  137 + x = 12 * 12
  137 + x = 144

• Subtract 137 from both sides to isolate 'x':

  x = 144 - 137
  x = 7

• Therefore, the value of the unknown number 'x' is 7.