Elementary Statistics 2nd Edition
Elementary Statistics 2nd Edition
2nd Edition
ISBN: 9781259724275
Author: William Navidi, Barry Monk
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 3, Problem 7RE

Measure that ball: Each of 16 students measured the circumference of a tennis ball by two different methods:

A: Estimate the circumference by eye.

B: Measure the circumference by rolling the

The results (in centimeters) are given below, in increasing order for each method

Chapter 3, Problem 7RE, Measure that ball: Each of 16 students measured the circumference of a tennis ball by two different

  1. Compute the sample standard deviation of the measurements for each method.
  2. For which method is the sample standard deviation larger? Why should one expect this method to have the larger standard deviation?
  3. Other things being equal, is it better for a measurement method to have a smaller standard deviation or a larger standard deviation? Or doesn’t it matter?

a)

Expert Solution
Check Mark
To determine

To find: The sample standard deviation for each method.

Answer to Problem 7RE

Sample standard deviation for method A is2.87

Sample standard deviation for method B is 0.75

Explanation of Solution

For Method A:

Given data:

    x
    18
    18
    18
    20
    22
    22
    22.5
    23
    24
    24
    25
    25
    25
    25
    26
    26.4

First, need to find the sample mean ( x¯ ).

Formula:

  x¯=i=1nXin

Here n = 16 which is the count of measurements.

Values of xi are measurements.

Calculation:

  x¯=363.916=22.74

Creating a table for finding population standard deviation:

    xxx¯(xx¯)2
    18-4.7422.47
    18-4.7422.47
    18-4.7422.47
    20-2.747.51
    22-0.740.55
    22-0.740.55
    22.5-0.240.06
    230.260.07
    241.261.59
    241.261.59
    252.265.11
    252.265.11
    252.265.11
    252.265.11
    263.2610.63
    26.43.6613.40
    Sum123.76

The formula of sample standard deviation:

  s= ( x i x ¯ ) 2 n1

Calculation:

From the table,

  (xix¯)2=123.76

Put in a formula,

  s=123.7616=2.87

Sample standard deviation = s = 2.87

For method B:

Given data

    x
    20
    20
    20
    20
    20.2
    20.5
    20.5
    20.7
    20.7
    20.7
    21
    21.1
    21.5
    21.6
    22.1
    22.3

Calculated sample mean is,

  x¯=332.916=20.81

Creating a table for finding population standard deviation:

    xxx¯(xx¯)2
    20-0.810.66
    20-0.810.66
    20-0.810.66
    20-0.810.66
    20.2-0.610.37
    20.5-0.310.10
    20.5-0.310.10
    20.7-0.110.01
    20.7-0.110.01
    20.7-0.110.01
    210.190.04
    21.10.290.08
    21.50.690.48
    21.60.790.62
    22.11.291.66
    22.31.492.22
    Sum8.33

Calculation:

From table,

  (xix¯)2=8.33

Put in a formula,

  s=8.3316=0.75

Sample standard deviation = 0.75

(b)

Expert Solution
Check Mark
To determine

To check: The standard deviation that is larger.

Answer to Problem 7RE

The standard deviation of method A is larger than method B.

Explanation of Solution

The standard deviation of method A is 2.87.

The standard deviation of method B is 0.75

From the above observation, it seems that the standard deviation of method A is larger than method B. As there is high variation in the measurement of method A which leads high standard deviation. The high standard deviation indicates that the data points are spread out over a large range of values.Method A is just by observational measurements which may lead to high variations in measurements. But method B is measuring the circumference by rolling the ball along the ruler which leads to lower the standard deviation

(c)

Expert Solution
Check Mark
To determine

To justify the standard deviation that is better for the given methods.

Answer to Problem 7RE

Lower standard deviation is always better as the measurements tend to be very close to the mean.

Explanation of Solution

To expressing the variability of a population, the standard deviation is commonly used to measureconfidence in statistical conclusions.A low standard deviation indicates that the measurements tend to be very close to the mean and a high standard deviation indicates that the measurements are spread out over a large range of values.Method A is just by observational measurements which may lead to high variations in measurements. But method B is measuring the circumference by rolling the ball along the ruler which leads to lower the standard deviation.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 3 Solutions

Elementary Statistics 2nd Edition

Ch. 3.1 - Find the mean, median, and mode for the following...Ch. 3.1 - Find the mean, median, and mode for the following...Ch. 3.1 - Prob. 19ECh. 3.1 - In Exercises 21—24, use the given frequency...Ch. 3.1 - In Exercises 21—24, use the given frequency...Ch. 3.1 - In Exercises 21—24, use the given frequency...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Find the mean, median, and mode of the data in the...Ch. 3.1 - Find the mean, median, and mode of the data in the...Ch. 3.1 - Facebook friends: In a study of Facebook users...Ch. 3.1 - Mean and median height: The National Center for...Ch. 3.1 - Prob. 31ECh. 3.1 - Greater swimmer: In the 2008 OIympic Games. Michel...Ch. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Heavy football players: Following are the weights,...Ch. 3.1 - Prob. 40ECh. 3.1 - Flu season: The following table presents the...Ch. 3.1 - News flash: The following table presents the...Ch. 3.1 - Commercial bank: Following arc amounts spend (in...Ch. 3.1 - Prob. 44ECh. 3.1 - Dont drink and drive: The Insurance Institute for...Ch. 3.1 - Prob. 46ECh. 3.1 - Be my Valentine: The following frequency...Ch. 3.1 - Get your degree: The following frequency...Ch. 3.1 - Prob. 49ECh. 3.1 - Take in a show: The following table presents the...Ch. 3.1 - Prob. 51ECh. 3.1 - Sources of news: A sample of 32 U.S. adults was...Ch. 3.1 - Find the mean: The National Center for Health...Ch. 3.1 - Find the median: According to a recent Current...Ch. 3.1 - Find the median: In a recent year, approximately...Ch. 3.1 - Find the median: The National Health and Nutrition...Ch. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - How many numbers? A data set has a median of 17,...Ch. 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 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - Find the sample variance and standard deviation...Ch. 3.2 - Find the sample variance and standard deviation...Ch. 3.2 - Find the sample variance and standard deviation...Ch. 3.2 - Find the population variance and standard...Ch. 3.2 - Find the population variance and standard...Ch. 3.2 - Find the population variance and standard...Ch. 3.2 - Approximate the sample variance and standard...Ch. 3.2 - Approximate the sample variance and standard...Ch. 3.2 - Approximate the population variance and standard...Ch. 3.2 - Approximate the population variance and standard...Ch. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Sports car or convertible? The following table...Ch. 3.2 - Heavy football players: Following are the weights,...Ch. 3.2 - Beer: The following table presents the number of...Ch. 3.2 - Whats your favorite TV show? The following table...Ch. 3.2 - House price: The following table presents price....Ch. 3.2 - Stock prices: Following are the closing prices of...Ch. 3.2 - Stocks or bonds? Following are the annual...Ch. 3.2 - Time to review: The following table presents the...Ch. 3.2 - Age distribution: The ages of residents of Banks...Ch. 3.2 - Lunch break: In a recent survey of 655 working...Ch. 3.2 - Pay your bills: In a large sample of customer...Ch. 3.2 - Newborn babies: A study conducted by the Center...Ch. 3.2 - Internet providers: In a survey of 600 homeowners...Ch. 3.2 - Lunch break: For the data in Exercise 41. Estimate...Ch. 3.2 - Pay your bill: For the data in Exercise 42....Ch. 3.2 - New born babies: For the data in Exercise 43....Ch. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Empirical Rule OK? The following histogram...Ch. 3.2 - Empirical Rule OK? The following histogram...Ch. 3.2 - Empirical Rule OK? The following histogram...Ch. 3.2 - Whats the temperature? The temperature in a...Ch. 3.2 - Find the standard deviation: The National Center...Ch. 3.2 - Find the standard deviation: The National Center...Ch. 3.2 - Price of electricity: The Energy Information...Ch. 3.2 - Possible or impossible? A data set has a mean of...Ch. 3.2 - Possible or impossible? A data set has a mean of...Ch. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Height and weight: A Naona1 Center for Health...Ch. 3.2 - Test scores: Scores on a statistics exam had a...Ch. 3.2 - Mean absolute deviation: A measure of spread that...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - A popu1aon has mean =7 and standard deviation =2....Ch. 3.3 - A population has mean =25 and standard deviation...Ch. 3.3 - In Exercises 19 and 20, identify the outlier. Then...Ch. 3.3 - Prob. 16ECh. 3.3 - For the data set 37 82 20 25 31 10 41 44 4 36 68...Ch. 3.3 - For the data set Find the first and third...Ch. 3.3 - For the data set Find the 58th percentile. Find...Ch. 3.3 - For the data set Find the 80th percentile. Find...Ch. 3.3 - Prob. 21ECh. 3.3 - A fish story: The mean length of one-year-old...Ch. 3.3 - Blood pressure in men: The three quartiles for...Ch. 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 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Bragging rights: After learning his score on a...Ch. 3.3 - Who scored the highest? On a final exam in a large...Ch. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 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 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - z-scores and skewed data: Table 3.9 presents the...Ch. 3 - Of the mean, median and mode, which must be a...Ch. 3 - The prices (in dollars) for a sample of personal...Ch. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 6CQCh. 3 - Each of the following histograms represents a data...Ch. 3 - In Exercises 8—11, suppose that the mean...Ch. 3 - Prob. 9CQCh. 3 - In Exercises 8—11, suppose that the mean...Ch. 3 - Prob. 11CQCh. 3 - Prob. 12CQCh. 3 - Prob. 13CQCh. 3 - Prob. 14CQCh. 3 - Prob. 15CQCh. 3 - Support your local artist: Following are the...Ch. 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 - Rivets: A machine makes rivets that are used in...Ch. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Advertising costs: The amounts spent (in billions)...Ch. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - The U.S. Department of Labor annually publishes an...Ch. 3 - Explain why the Empirical Rule is more useful than...Ch. 3 - Prob. 3WAICh. 3 - Prob. 4WAICh. 3 - Percentiles are values that divide a data set into...Ch. 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 - Electronic devices contain electric circuits...
Knowledge Booster
Background pattern image
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.
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License