/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 121. SD contest聽This is a standard d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q 121. (page 79)

SD contestThis is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.

(a) Choose four numbers that have the smallest possible standard deviation.

(b)Choose four numbers that have the largest possible standard deviation.

(c) Is more than one choice possible in either part (a) or (b)? Explain.

Short Answer

Expert verified

Part (a) 2, 2, 2, 2

Part (b) 0, 0, 10, 10

Part (c) There are multiple options available for (a) and part (b) unique.

Step by step solution

01

Part (a) Step 1. Given information.

The given statement says that we must select four digits from the range of 0 to 10, we can also repeat numbers.

02

Part (a) Step 2. Select four numbers that have the smallest possible standard deviation.

From the given set of data, the smallest possible standard deviation is 0 if we choose the four numbers like 2, 2, 2, 2.

We all know that standard deviation is nonnegative.

Therefore, the numbers are 2, 2, 2, and 2.

03

Part (b) Step 1. Select four numbers that have the largest possible standard deviation.

Getting the largest standard deviation is only possible when we have values that are far from the mean value.

The given numbers range from 0 to 10. Then the largest standard deviation will be possible if we choose two values as 0 and two other values as 10 because our mean will lie exactly in between which is 5.

Therefore, the numbers are 0, 0, 10, and 10.

04

Part (c) Step 1. State if more choices possible in either part (a) or (b).

Part (a) allows for several options because getting a standard deviation equal to 0 is possible if the sample contains one unique value.

Furthermore, in portion (a), we provided two options, implying that more than one option is available.

In Part (b), the answer is unique because changing only one of the variables changes the mean from 5 to a lower value, lowering the total deviation from the mean.

Because the standard deviation is proportional to the total deviation, the standard deviation will fall.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Birth days The frequency table summarizes data on the numbers of babies born on each day of the week in the United States in a recent week.

(a) Identify the individuals in this data set.

(b) Make a frequency bar graph to display the data. Describe what you see.

Risks of playing soccer (1.1) A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-fifties:

Part (a). What percent of the people in this study were elite soccer players? What percent of the people in this study developed arthritis?

Part (b). What percent of the elite soccer players developed arthritis? What percent of those who got arthritis were elite soccer players?

Part (c). Researchers suspected that the more serious soccer players were more likely to develop arthritis later in life. Do the data confirm this suspicion? Calculate appropriate percentages to support your answer.

Multiple Choice Select the best answer.

Exercises 9 and 10 refer to the following setting. At the Census Bureau website www.census.gov, you can view detailed data collected by the American Community Survey.

The following table includes data for 10 people chosen at random from the more than 1 million people in households contacted by the survey. 鈥淪chool鈥� gives the highest level of education completed.

This data set contains

(a) 7 variables, 2 of which are categorical.

(b) 7 variables, 1 of which is categorical.

(c) 6 variables, 2 of which are categorical.

(d) 6 variables, 1 of which is categorical.

(e) None of these.

Superpowers A total of 415 children from the United Kingdom and the United States who completed a survey in a recent year were randomly selected. Each student鈥檚 country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the following table.

(a) What proportion of students in the sample are from the United States?

(b) Find the distribution of superpower preference for the students in the sample using relative frequencies.

(c) What percent of students in the sample are from the United Kingdom and prefer telepathy as their superpower preference?

Women and children first? Here鈥檚 another table that summarizes data on survival status by gender and class of travel on the Titanic:

(a) Find the distributions of survival status for males and for females within each class of travel. Did women survive the disaster at higher rates than men? Explain.

(b) In an earlier example, we noted that survival status is associated with class of travel. First-class passengers had the highest survival rate, while third-class passengers had the lowest survival rate. Does this same relationship hold for both males and females in all three classes of travel? Explain.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.