GATE DS&AI 2024 | Question: 24

Question

The sample average of $50$ data points is $40$. The updated sample average after including a new data point taking the value of $142$ is $\_\_\_\_\_\_\_\_$.

Comments

the question had mentioned "sample" twice so, i deliberately took $n-1$ in the denominator.

Answer 1

To find the updated sample average after including a new data point, you need to use the formula for calculating the sample average:

\[ \text{New average} = \frac{( \text{Old average} \times \text{Number of data points}) + \text{New data point}}{\text{Number of data points} + 1} \]

Given:

Old average = 40

Number of data points = 50

New data point = 142

Let's substitute these values into the formula:

\[ \text{New average} = \frac{(40 \times 50) + 142}{50 + 1} \]

\[ = \frac{(2000 + 142)}{51} \]

\[ = \frac{2142}{51} \]

\[ \approx 42 \]

Therefore, the updated sample average after including the new data point is approximately 42.

Answer 2

ANOTHER WAY:- 

1. The original sum of the 50 data points is 50 × 40 = 2000.
2. Adding the new data point (142) makes the new sum as 2000 + 142 = 2142.
3. Now, instead of 50 numbers, we have 51.
4. The new average will become 2142/51 = 42

Hence, The updated sample average after including a new data point taking the value of 142 is 42. 

 

Answer 3

Updated Sample Average = Old sample average + (value of new data included - old sample average)/(total no. of  data points )

Here,  old sample average = 40

           value of new data included = 142

          total no. of data points after adding new data = 50 +1 =51

so, Updated sample average = 40 + ( 142 - 40)/51 = 42