Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Textbook Question
Chapter 3, Problem 1CQ
Of the
Expert Solution & Answer
To determine
Find the measure which must be a value in the data set.
Answer to Problem 1CQ
The mode must appear in the data set.
Explanation of Solution
Mean:
The arithmetic mean (also called the mean) is the most commonly used measure of central tendency. It is calculated by summing the observed numerical values of a variable in a set of data and then dividing the total by the number of observations involved.
Computation of mean:
If
The mean value is calculated as,
Therefore, mean is the average of all values. Sometimes the data set contains the mean but it is not possible that always mean value will be an observation in the data.
Median:
The median is the middle most value of the observation. In case of no tie, half of the observations will be less than middle most value, and half of the observations will be greater than that value. In addition, the median is unaffected by extreme values in a set of data.
Let
The steps for finding the median:
- The all data values should be arranged in ascending order.
- If the total number of data values, n is odd, then the median will be the middle value or if n is even, then the median will be the average of middle two values.
Hence, it can be said that the median is actually the middle value that divides the whole data set in two parts. For an even sample size, the median will be average. Hence, median does not appear in the data.
Mode:
Occasionally, when describing a set of data, the mode is used as a measure of central tendency. The mode is the most frequently occurring value in a data set. The mode can often be identified by referring to a histogram or polygon. Distributions with a single mode are referred to as unimodal. Distributions with two modes are referred to as bimodal.
Therefore, mode is the data value with maximum frequency. Hence, mode appears in the data.
- Hence, it can be said that mode must appear in the data set compared to mean, median and mode.
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Chapter 3 Solutions
Essential Statistics
Ch. 3.1 - 1. Compute the mean and median of the following...Ch. 3.1 - 2. Compute the mean and median of the following...Ch. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - 5. A data set has a mean of 5 and a median of 7....Ch. 3.1 - Prob. 6CYUCh. 3.1 - In Exercises 7–10, fill in each blank with the...Ch. 3.1 - In Exercises 7–10, fill in each blank with the...Ch. 3.1 - In Exercises 7–10, fill in each blank with the...Ch. 3.1 - In Exercises 7–10, fill in each blank with the...
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - 18. Find the mean, median, and mode for the...Ch. 3.1 - Prob. 19ECh. 3.1 - In Exercises 19–22, use the given frequency...Ch. 3.1 - Prob. 21ECh. 3.1 - In Exercises 19–22, use the given frequency...Ch. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - 30. Mean and median height: The National Center...Ch. 3.1 - 31. Hamburgers: An ABC News story reported the...Ch. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - 36. Beer: The following table presents the number...Ch. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - 39. Heavy football players: Following are the...Ch. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - 42. News flash: The following table presents the...Ch. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - 52. Sources of news: A sample of 32 U.S. adults...Ch. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Prob. 74ECh. 3.2 - 1. Compute the population variance for the St....Ch. 3.2 - Prob. 2CYUCh. 3.2 - Prob. 3CYUCh. 3.2 - Prob. 4CYUCh. 3.2 - Prob. 5CYUCh. 3.2 - Prob. 6CYUCh. 3.2 - Prob. 7CYUCh. 3.2 - Prob. 8CYUCh. 3.2 - Prob. 9ECh. 3.2 - In Exercises 9–12, fill in each blank with the...Ch. 3.2 - Prob. 11ECh. 3.2 - In Exercises 9–12, fill in each blank with the...Ch. 3.2 - Prob. 13ECh. 3.2 - In Exercises 13–16, determine whether the...Ch. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - 18. Find the sample variance and standard...Ch. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - 23. Approximate the sample variance and standard...Ch. 3.2 - 24. Approximate the sample variance and standard...Ch. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - 33. Heavy football players: Following are the...Ch. 3.2 - 34. Beer: The following table presents the number...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - 42. Pay your bills: In a large sample of customer...Ch. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - 46. Pay your bills: For the data in Exercise 42,...Ch. 3.2 - Prob. 47ECh. 3.2 - 48. Internet providers: For the data in Exercise...Ch. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.3 - Following are final exam scores, arranged in...Ch. 3.3 - Prob. 2CYUCh. 3.3 - Prob. 3CYUCh. 3.3 - Prob. 4CYUCh. 3.3 - Prob. 5ECh. 3.3 - In Exercises 5–8, fill in each blank with the...Ch. 3.3 - Prob. 7ECh. 3.3 - In Exercises 5–8, fill in each blank with the...Ch. 3.3 - Prob. 9ECh. 3.3 - In Exercises 9–12, determine whether the statement...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - A population has mean μ = 7 and standard deviation...Ch. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - For the data set a. Find the 80th percentile. b....Ch. 3.3 - Standardized tests: In a recent year, the mean...Ch. 3.3 - A fish story: The mean length of one-year-old...Ch. 3.3 - Prob. 23ECh. 3.3 - Blood pressure in women: The article referred to...Ch. 3.3 - Hazardous waste: Following is a list of the number...Ch. 3.3 - Cholesterol levels: The National Health and...Ch. 3.3 - Commuting to work: Jamie drives to work every...Ch. 3.3 - Windy city by the bay: Following are wind speeds...Ch. 3.3 - Caffeine: Following are the number of grams of...Ch. 3.3 - Nuclear power: The following table presents the...Ch. 3.3 - Place your bets: Recently, 28 states in the U.S....Ch. 3.3 - Hail to the chief: There have been 57 presidential...Ch. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Automotive emissions: Following are levels of...Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Boxplot possible? Following is the five-number...Ch. 3.3 - Unusual boxplot: Ten residents of a town were...Ch. 3.3 - Prob. 42ECh. 3.3 - The vanishing outlier: Seven families live on a...Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3 - Of the mean, median, and mode, which must be a...Ch. 3 - Prob. 2CQCh. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 6CQCh. 3 - Each of the following histograms represents a data...Ch. 3 - Prob. 8CQCh. 3 - Prob. 9CQCh. 3 - Prob. 10CQCh. 3 - Prob. 11CQCh. 3 - Prob. 12CQCh. 3 - Prob. 13CQCh. 3 - Prob. 14CQCh. 3 - Prob. 15CQCh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Measure that ball: Each of 16 students measured...Ch. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - How long can you talk? A manufacturer of cell...Ch. 3 - Prob. 11RECh. 3 - Advertising costs: The amounts spent (in billions)...Ch. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 1WAICh. 3 - Explain why the Empirical Rule is more useful than...Ch. 3 - Prob. 3WAICh. 3 - Prob. 4WAICh. 3 - Prob. 5WAICh. 3 - Prob. 1CSCh. 3 - Prob. 2CSCh. 3 - Prob. 3CSCh. 3 - Prob. 4CSCh. 3 - Prob. 5CSCh. 3 - Prob. 6CSCh. 3 - Prob. 7CSCh. 3 - Prob. 8CSCh. 3 - Prob. 9CS
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