Question

The mean of $ 19 $ observations is $ 4 $ . If one more observation of $ 24 $ is added to the data, the new mean will be:
A. $ 4 $
B. $ 5 $
C. $ 6 $
D. $ 7 $

Answer 1

Hint: Mean can be defined as the sum of all the numbers upon the total number of the numbers. Mean is affected by all the values of the sequences, here we will use the number of given observations. We will convert the given word statement in the form of mathematical expressions and then will find the new mean.

Complete step-by-step answer:
Mean is expressed as the ratio of the sum of all the observations upon the number of observations.
Given that: The mean of $ 19 $ observations is $ 4 $ .
Let us assume the sum of observations be “x”
 $ \overline x = \dfrac{{\sum {{x_i}} }}{n} $
Place the values in the above expression –
 $ 4 = \dfrac{x}{{19}} $
Cross multiplication where the numerator of one side is multiplied with the denominator of the opposite side.
 $ \Rightarrow x = 19 \times 4 $
Find the product of the terms in the above equation.
 $ \Rightarrow x = 76 $
If one more observation of $ 24 $ is added to the data, the new mean,
 $ \overline {{x_N}} = \dfrac{{76 + 24}}{{20}} $
Simplify the above equation –
 $ \overline {{x_N}} = \dfrac{{100}}{{20}} $
Find the factors for the term in numerator,
 $ \overline {{x_N}} = \dfrac{{5 \times 20}}{{20}} $
Common multiple from the numerator and the denominator cancels each other.
 $ \overline {{x_N}} = 5 $
Hence, from the given multiple choices the option B is the correct answer.
So, the correct answer is “Option B”.

Note: Do not get confused between the terms and the symbols of mean between the data are from a sample and population. If the data are from a sample, then the mean is denoted by $ \overline x $ whereas, if the data are from a population, then the mean is denoted by $ \mu $ .