Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10 a. Find the value of the population median. 4 (Type an integer or a decimal. Do not round.) b. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Sample Median Probability 1 ▼ ▼ ▼ ■ ▼ (Type integers or simplified fractions.)
Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10 a. Find the value of the population median. 4 (Type an integer or a decimal. Do not round.) b. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Sample Median Probability 1 ▼ ▼ ▼ ■ ▼ (Type integers or simplified fractions.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Educational Content: Exploring Sampling and Medians**
In this exercise, we'll explore how to find the population median and understand sampling distributions through a practical example.
### Problem Overview
Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assuming that samples of size n = 2 are randomly selected with replacement from this population (ages: 1, 4, and 10), the table below shows nine different samples obtained.
**Samples:**
- (1, 1)
- (1, 4)
- (1, 10)
- (4, 1)
- (4, 4)
- (4, 10)
- (10, 1)
- (10, 4)
- (10, 10)
Use these to complete parts (a) and (b).
### Part (a)
**Find the value of the population median.**
- **Solution:** The population ages are 1, 4, and 10. The median can be determined by arranging the numbers in order and selecting the middle value.
- Ordered ages: 1, 4, 10
- **Population Median:** 4
- *(Type an integer or a decimal. Do not round.)*
### Part (b)
**Find the median of each of the nine samples, then summarize the sampling distribution of the medians in a table showing the probability distribution of distinct median values.**
| Sample Median | Probability |
|---------------|-------------|
| | |
| | |
| | |
| | |
| | |
- **Instructions:** Determine the median for each sample pair, and calculate the probability for each median value based on the total number of samples (9). Enter the medians and probabilities as appropriate, using integers or simplified fractions.
This exercise highlights the process of determining medians from samples and understanding how these medians distribute across a population. It provides insights into statistical concepts relevant in real-world data analysis.
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