Explanation Median: When the sample size is even the median is the average of middle two values in the sample. The probability for an event e is, P ( event E ) = N e N Where, N e : Number of favorable events N : Total number of outcomes The first possible for the sample size 4 from a population of eight measurements is ( 2 , 6 , 9 , 12 ) . The median for the first sample is, M = 6 + 9 2 = 15 2 = 7.5 Similarly the remaining samples with their corresponding medians are: Sample Median ( M ) Sample Median ( M ) Sample Median ( M ) 2, 6, 9, 12 7.5 2, 12, 25, 29 18.5 6, 12, 39, 50 25.5 2, 6, 9, 25 7.5 2, 12, 25, 39 18.5 6, 25, 29, 39 27 2, 6, 9, 29 7.5 2, 12, 25, 50 18.5 6, 25, 29, 50 27 2, 6, 9, 39 7.5 2, 12, 29, 39 20.5 6, 25, 39, 50 32 2, 6, 9, 50 7.5 2, 12, 29, 50 20.5 6, 29, 39, 50 34 2, 6, 12, 25 9 2, 12, 39, 50 25.5 9, 12, 25, 29 18.5 2, 6, 12, 29 9 2, 25, 29, 39 27 9, 12, 25, 39 18.5 2, 6, 12, 39 9 2, 25, 29, 50 27 9, 12, 25, 50 18.5 2, 6, 12, 50 9 2, 25, 39, 50 32 9, 12, 29, 39 20.5 2, 6, 25, 29 15.5 2, 29, 39, 50 34 9, 12, 29, 50 20.5 2, 6, 25, 39 15.5 6, 9, 12, 25 10.5 9, 12, 39, 50 25.5 2, 6, 25, 50 15.5 6, 9, 12, 29 10.5 9, 25, 29, 39 27 2, 6, 29, 39 17.5 6, 9, 12, 39 10.5 9, 25, 29, 50 27 2, 6, 29, 50 17.5 6, 9, 12, 50 10.5 9, 25, 39, 50 32 2, 6, 39, 50 22.5 6, 9, 25, 29 17 9, 29, 39, 50 34 2, 9, 12, 25 10.5 6, 9, 25, 39 17 12, 25, 29, 39 27 2, 9, 12, 29 10.5 6, 9, 25, 50 17 12, 25, 29, 50 27 2, 9, 12, 39 10.5 6, 9, 29, 39 19 12, 25, 39, 50 32 2, 9, 12, 50 10.5 6, 9, 29, 50 19 12, 29, 39, 50 34 2, 9, 25, 29 17 6, 9, 39, 50 24 25, 29, 39, 50 34 2, 9, 25, 39 17 6, 12, 25, 29 18.5 2, 9, 25, 50 17 6, 12, 25, 39 18.5 2, 9, 29, 39 19 6, 12, 25, 50 18.5 2, 9, 29, 50 19 6, 12, 29, 39 20.5 2, 9, 39, 50 24 6, 12, 29, 50 20.5 It is clear that there are 70 samples of size 4, than the probability of drawing first sample is. P ( y 1 ) = 1 70 This indicates that the sample median 7.5 with probability 1 70 . Similarly for the remaining samples are, Median ( M ) P ( M ) Median ( M ) P ( M ) Median ( M ) P ( M ) 7.5 1 70 18.5 1 70 25.5 1 70 7.5 1 70 18.5 1 70 27 1 70 7.5 1 70 18.5 1 70 27 1 70 7.5 1 70 20.5 1 70 32 1 70 7.5 1 70 20.5 1 70 34 1 70 9 1 70 25.5 1 70 18.5 1 70 9 1 70 27 1 70 18.5 1 70 9 1 70 27 1 70 18

An Introduction to Statistical Methods and Data Analysis

7th Edition

ISBN: 9781305269477

Author: R. Lyman Ott, Micheal T. Longnecker

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Videos

Question

Chapter 4.18, Problem 106SE

To determine

Find the sampling distribution for the sample median.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.18, Problem 105SE

Chapter 4.18, Problem 107SE

Students have asked these similar questions

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per Minute Class Frequency 51-58 5 59-66 8 67-74 9 75-82 7 83-90 8

can someone solve

QUAT6221wA1 Accessibility Mode Immersiv Q.1.2 Match the definition in column X with the correct term in column Y. Two marks will be awarded for each correct answer. (20) COLUMN X Q.1.2.1 COLUMN Y Condenses sample data into a few summary A. Statistics measures Q.1.2.2 The collection of all possible observations that exist for the random variable under study. B. Descriptive statistics Q.1.2.3 Describes a characteristic of a sample. C. Ordinal-scaled data Q.1.2.4 The actual values or outcomes are recorded on a random variable. D. Inferential statistics 0.1.2.5 Categorical data, where the categories have an implied ranking. E. Data Q.1.2.6 A set of mathematically based tools & techniques that transform raw data into F. Statistical modelling information to support effective decision- making. 45 Q Search 28 # 00 8 LO 1 f F10 Prise 11+

Chapter 4 Solutions

An Introduction to Statistical Methods and Data Analysis

Ch. 4.18 - Indicate which interpretation of the probability...Ch. 4.18 - If you are having a stroke, it is critical that...Ch. 4.18 - In reporting highway safety, the National Highway...Ch. 4.18 - In a cable TV program concerning the risk of...Ch. 4.18 - The gaming commission in its annual examination of...Ch. 4.18 - The state vehicle inspection bureau provided the...Ch. 4.18 - The Texas Lottery has a game, Daily 4, in which a...Ch. 4.18 - A die is rolled two times. Provide a list of the...Ch. 4.18 - Refer to Exercise 4.10. Assume that the die is a...Ch. 4.18 - Refer to Exercise 4.11. a. Describe the event that...

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Find the sampling distribution for the sample median .

Concept explainers

Videos

Find the sampling distribution for the sample median.

Want to see the full answer?

Chapter 4 Solutions