STATISTICAL TECHNIQUES-ACCESS ONLY
STATISTICAL TECHNIQUES-ACCESS ONLY
16th Edition
ISBN: 9780077639648
Author: Lind
Publisher: MCG
bartleby

Videos

Question
Book Icon
Chapter 3, Problem 83CE

a.

To determine

Find the mean of the number of items.

Find the median of the number of items.

a.

Expert Solution
Check Mark

Answer to Problem 83CE

The mean of the number of items is 9.1.

The median of the number of items is 9.

Explanation of Solution

Calculation:

Step by step procedure to obtain mean, median using MINITAB software is given as,

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the column Number of Items.
  • Choose option statistics, and select Mean and Median.
  • Click OK.

Output using MINITAB software is given below:

STATISTICAL TECHNIQUES-ACCESS ONLY, Chapter 3, Problem 83CE , additional homework tip  1

Hence, the mean of the number of items is 9.1, and the median of the number of items is 9.

b.

To determine

Find the range of the number of items.

Find the standard deviation of the number of items.

b.

Expert Solution
Check Mark

Answer to Problem 83CE

The range of the number of items is 14.

The standard deviation of the number of items is 3.566.

Explanation of Solution

Calculation:

Step by step procedure to obtain standard deviation and range using MINITAB software is given as,

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the column Number of Items.
  • Choose option statistics, and select standard deviation and range.
  • Click OK.

Output using MINITAB software is given below:

STATISTICAL TECHNIQUES-ACCESS ONLY, Chapter 3, Problem 83CE , additional homework tip  2

Hence, the range of the number of items is 14 and standard deviation of the number of items is 3.566.

c.

To determine

Find the frequency distribution for number of items.

c.

Expert Solution
Check Mark

Answer to Problem 83CE

The frequency distribution for number of items is,

ClassFrequency
3.5-6.510
6.5-9.56
9.5-12.59
12.5-15.54
15.5-18.51
Total30

Explanation of Solution

Calculation:

Selection of number of classes:

The “2 to the k rule” suggests that the number of classes is the smallest value of k, where 2k is greater than the number of observations.

Formula for class interval:

The formula for the class interval is given as follows:

i(Maximum valueMinimum value)k

Frequency distribution:

The frequency table is a collection of mutually exclusive and exhaustive classes that show the number of observations in each class.

Where, i is the class interval and k is the number of classes.

The data set consists of 30 observations. The value of k can be obtained as follows:

24=16<3025=32>30

Here, k=5 is the smallest value for which 2k is greater than the number of observations. The number of classes for the given data set is 5.

The class interval is,

i(Maximum valueMinimum value)k18451452.8

In practice, the class interval size is usually rounded up to some convenient number. Thus, the reasonable class interval is 3.

Since the minimum value is 4 and the class interval is 3, the first class would be 3.5-6.5.

The frequency distribution for duration in minutes can be constructed as follows:

ClassFrequency
3.5-6.510
6.5-9.56
9.5-12.59
12.5-15.54
15.5-18.51
Total30

d.

To determine

Find the mean of the data.

Find the standard deviation of the data.

Compare these values with those computed in Part (a).

Explain why the values are different

d.

Expert Solution
Check Mark

Answer to Problem 83CE

The mean of the data is 9.

The standard deviation of the data is 3.553.

Explanation of Solution

Arithmetic mean of grouped data:

The mean of the data that is given in frequency distribution (grouped data) is calculated as,

x¯=fMn

In the formula, x¯ denotes the sample mean, M denotes the midpoint for each class, f denotes the frequency for each class, n denotes the total frequency.

Midpoint:

The midpoint is the average of the lower class limits of two consecutive classes. The formula is,

Midpoint=Lowerlimitofclass+Lowerlimitofconsecutiveclass2

The frequency distribution table for mean is,

Class

Frequency

f

MfM
3.5-6.510550
6.5-9.56848
9.5-12.591199
12.5-15.541456
15.5-18.511717
n=30fM=270

Substitute n=30 and fM=270 in arithmetic mean formula.

x¯=27030=9

Hence, the mean of the data is 9.

Standard deviation of grouped data:

The standard deviation of the data that is given in frequency distribution (grouped data) is calculated as,

s=f(Mx¯)2n1

In the formula, s denotes the sample standard deviation, x¯ denotes the sample mean of grouped data, M denotes the midpoint for each class, f denotes the frequency for each class, n denotes the total frequency.

The value of mean is 9. The frequency distribution table for standard deviation is,

Class

Frequency

f

M(Mx¯)(Mx¯)2f(Mx¯)2
3.5-6.5105–416160
6.5-9.568–116
9.5-12.59112436
12.5-15.5414525100
15.5-18.511786464
n=30f(Mx¯)2=366

Substitute n=30 and f(Mx¯)2=366, in standard deviation formula.

s=366301=36629=12.6206896=3.553

Hence, the standard deviation of the data is 3.553.

The mean value is same for normal method and frequency distribution. But there is a slight change in the value of the standard deviation. This difference is due to using grouped data in frequency distribution. The frequency distribution only gives the estimate of the standard deviation because actual values of the data are not used.

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!
Students have asked these similar questions
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…
If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9.   The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24?   The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…

Chapter 3 Solutions

STATISTICAL TECHNIQUES-ACCESS ONLY

Ch. 3 - For Exercises 710, (a) compute the arithmetic mean...Ch. 3 - Prob. 10ECh. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 2.1SRCh. 3 - The number of work stoppages in the automobile...Ch. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Sally Reynolds sells real estate along the coastal...Ch. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 3SRCh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 4SRCh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 5.1SRCh. 3 - Prob. 5.2SRCh. 3 - Compute the geometric mean of the following...Ch. 3 - Prob. 28ECh. 3 - Listed below is the percent increase in sales for...Ch. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 6SRCh. 3 - Prob. 35ECh. 3 - Prob. 36ECh. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40ECh. 3 - Prob. 7SRCh. 3 - Prob. 41ECh. 3 - Prob. 42ECh. 3 - Prob. 43ECh. 3 - Prob. 44ECh. 3 - Plywood Inc. reported these returns on stockholder...Ch. 3 - Prob. 46ECh. 3 - Prob. 8SRCh. 3 - Prob. 47ECh. 3 - Prob. 48ECh. 3 - Prob. 49ECh. 3 - Prob. 50ECh. 3 - Prob. 51ECh. 3 - Prob. 52ECh. 3 - Prob. 9SRCh. 3 - Prob. 53ECh. 3 - The mean income of a group of sample observations...Ch. 3 - Prob. 55ECh. 3 - Prob. 56ECh. 3 - Prob. 10SRCh. 3 - Prob. 57ECh. 3 - Prob. 58ECh. 3 - Estimate the mean and the standard deviation of...Ch. 3 - Prob. 60ECh. 3 - The IRS was interested in the number of individual...Ch. 3 - Prob. 62ECh. 3 - Prob. 63CECh. 3 - Prob. 64CECh. 3 - Prob. 65CECh. 3 - Prob. 66CECh. 3 - Prob. 67CECh. 3 - Prob. 68CECh. 3 - Prob. 69CECh. 3 - Prob. 70CECh. 3 - Prob. 71CECh. 3 - Prob. 72CECh. 3 - Prob. 73CECh. 3 - A recent article suggested that, if you earn...Ch. 3 - Prob. 75CECh. 3 - Prob. 76CECh. 3 - Prob. 77CECh. 3 - Prob. 78CECh. 3 - The Apollo space program lasted from 1967 until...Ch. 3 - Prob. 80CECh. 3 - Prob. 81CECh. 3 - The Kentucky Derby is held the first Saturday in...Ch. 3 - Prob. 83CECh. 3 - Prob. 84CECh. 3 - Bidwell Electronics Inc. recently surveyed a...Ch. 3 - Refer to the Real Estate data, which reports...Ch. 3 - Refer to the Baseball 2012 data, which report...Ch. 3 - Refer to the Buena School District bus data....
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License