Statistics
Statistics
nta_abhyas_2025
Grade None
Question:
The mean of a data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data is
Step-by-Step Solution
Key Concept: The mean of a dataset is the sum of all observations divided by the count of observations.
Given: $\left(\frac{\sum x_i}{n}\right) \cdot 16 = 16$. Therefore $\sum x_i = 16n$. We have $\sum x_i^2 = 240$ and the relationship $\sum x_i = 240$. The required mean is $\frac{\sum x_i + 3 + 4 + 5}{15} = \frac{240 + 12}{15} = \frac{252}{15} = 16.8$.
Correct Answer: 1