Question

The mean of 994, 996, 998, 1000, and 1002 are
A. 992
B. 1004
C. 998
D. 999

Answer 1

First, find the sum of these terms. After that use the mean formula which is the average of the sum of the terms and is calculated by $\bar x = \dfrac{{\sum {{x_i}} }}{n}$. Then substitute the sum of the terms and the total number of terms. Then, do the simplification to get the mean of the numbers.

Complete step-by-step solution:
The given numbers are 994, 996, 998, 1000, and 1002.
We have to find the mean of these numbers.
Mean is the measure of the average of a set of values which can be calculated by dividing the sum of all the observations by the number of observations. There are four different ways to measure the mean of a data set. They are arithmetic mean, geometric mean, harmonic mean, and weighted arithmetic mean. Usually, the arithmetic mean is calculated because it is easy to calculate.
The mean is calculated by dividing the sum of observations by the number of observations. The formula is given by,
$\bar x = \dfrac{{\sum {{x_i}} }}{n}$
We will find the sum of terms by adding all the first numbers.
$\Rightarrow \sum {{x_i}} = 994 + 996 + 998 + 1000 + 1002$
Add the terms on the right side,
$\Rightarrow \sum {{x_i}} = 4990$
Now, substitute the value in the mean formula,
$\Rightarrow \bar x = \dfrac{{4990}}{5}$
Divide the numerator by denominator,
$\therefore \bar x = 998$
Thus, the mean of the numbers is 998.

Hence, option (C) is correct.

Note: Whenever we face such types of problems the key point that we need to recall is that Mean or Arithmetic mean is the average of given numbers. It is found by calculating the sum of the given numbers and dividing it by how many numbers there are. These types of questions are based only on this definition and can be easily solved using this.