Question

The mean of 10 observations is 15.7. If a new observation 19 is included, the new mean is ___
(a) 17.6
(b) 16
(c) 13.8
(d) 34.7

Answer 1

We will first find the sum of initial observations as the product of mean and number of observations. Then, add the new observation to find the new sum of observations. Next, divide the sum of observations by a new number of observations to find the new mean.

Complete step by step solution:
We are given that the mean of 10 observations is 15.7
We know that the mean is calculated by dividing the sum of observations by the number of observations.
That is, the sum of observations is the product of mean and number of observations.
Therefore, the sum of observations is $10 \times 15.7 = 157$
Also, we are given that a new observation 19 is included, then the sum of the observations will be
$157 + 19 = 176$
Also, there is an increase in the number of observations by 1.
The new number of observation is 11.
Now, mean can be calculated using the formula,
$\dfrac{{{\text{Sum of observation}}}}{{{\text{Number of observation}}}}$
That is, $\dfrac{{176}}{{11}} = 16$
Hence, the new mean is 16.

Thus, option B is the correct answer.

Note:
Mean is also known as the average of numbers. Many students make mistake by considering an increase in the number of terms when a new term is added to the number of observations. One has to take care that the sum and number of observations both will change when a new observation is added.