Solved Examples on Point Estimation
Example 1: Calculate the sample mean for the following data set: {12, 15, 18, 21, 24}.
Solution:
Step 1: Add up all the values: 12 + 15 + 18 + 21 + 24 = 90.
Step 2: Divide the sum by the number of observations: 90 / 5 = 18.
Therefore, the sample mean is 18.
Example 2: Find the sample variance for the data set: {5, 8, 10, 12, 15}.
Solution:
Step 1: Calculate the sample mean using the same process as in the previous question. Mean = (5 + 8 + 10 + 12 + 15) / 5 = 50 / 5 = 10.
Step 2: Calculate the squared differences between each observation and the mean: (5 – 10)² + (8 – 10)² + (10 – 10)² + (12 – 10)² + (15 – 10)² = 25 + 4 + 0 + 4 + 25 = 58.
Step 3: Divide the sum of squared differences by the number of observations minus 1: 58 / (5 – 1) = 58 / 4 = 14.5.
Therefore, the sample variance is 14.5.
Example 3: Determine the sample proportion of successes if out of 50 trials, 30 were successful.
Solution:
Divide the number of successful trials by the total number of trials: 30 / 50 = 0.6.
Therefore, the sample proportion of successes is 0.6 or 60%.
Example 4: Calculate the sample median for the following data set A: {10, 15, 18, 20, 22}.
Solution:
Since, data set has an odd number of observations, the median is the middle value after arranging in ascending or descending order.
A = {10, 15, 18, 20, 22}
n = 5
It is already in descending order
Median = {(n + 1)/2}th term
Median = (5 + 1)/2 = 3rd term = 18
Example 5: Find the sample standard deviation for the data set: {3, 5, 7, 9, 11}.
Solution:
Step 1: Calculate the sample mean: (3 + 5 + 7 + 9 + 11) / 5 = 7.
Step 2: Calculate the squared differences between each observation and the mean: (3 – 7)² + (5 – 7)² + (7 – 7)² + (9 – 7)² + (11 – 7)² = 16 + 4 + 0 + 4 + 16 = 40.
Step 3: Divide the sum of squared differences by the number of observations minus 1: 40 / (5 – 1) = 40 / 4 = 10.
Step 4: Take the square root of the result: √10 ≈ 3.16.
Therefore, the sample standard deviation is approximately 3.16.
Point Estimation
Point estimation is a fundamental concept in statistics providing a method for estimating population parameters based on sample data. In this article, we will discuss point estimation, its techniques and its significance in detail.
Table of Content
- What is Point Estimation in Statistics?
- Properties of Point Estimators
- Methods Used to Calculate Point Estimators
- Formulae to Measure Point Estimators
- Solved Examples on Point Estimation
- Practice Problems on Point Estimation
- FAQs on Point Estimation