Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q 96. (page 75)

ShakespeareThe histogram shows the distribution of lengths of words used in Shakespeare’s plays.

(a) Find the median word length in Shakespeare’s plays from the histogram. Explain your method clearly.

(b) Calculate the mean of the distribution. Show your work.

Short Answer

Expert verified

Part (a) 4 words.

Part (b) 4.13 words

Step by step solution

01

Part (a) Step 1. Given information.

The given histogram is shown below with their frequency:

02

Part (a) Step 2. Find the median word length in Shakespeare’s plays from the histogram. 

As we know that median is the middle value of a data set. As the given set is even, the median will be the average of two middle values (50th and 51st) of this sorted data.

Because 5+17+22=44(sum frequencies first three bars) and 5+17+22+23=67(sum frequencies first four bars), the 50th and 51st data values are both equal to 4 in the histogram's third bar.

M=4+42=4

The median units are the same as the data values' units, so the median is 4 words.

03

Part (b) Step 1. Calculate the mean of the distribution.

Word Length (x)Frequency (f)fx
155
21734
32266
42392
51260
6742
7535
8432
9327
10220
Total100413

x¯=∑fxn=413100=4.13

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Binge-watchingDo you “binge-watch” television series by viewing multiple episodes of a series at one sitting? A survey of 800 people who binge-watch were asked how many episodes is too many to watch in one viewing session. The results are displayed in the bar graph. Explain how this graph is misleading.

Who studies more? Researchers asked the students in a large first-year college class how many minutes they studied on a typical weeknight. The back-to-back stemplot displays the responses from random samples of 30 women and 30 men from the class, rounded to the nearest 10 minutes. Write a few sentences comparing the male and female distributions of study time.

Feeling sleepy? Refer to Exercise 45. Describe the shape of the distribution.

Women and children first? Here’s 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.

Returns on common stocks The return on a stock is the change in its market price plus Page Number: 51 any dividend payments made. Return is usually expressed as a percent of the beginning price. The figure shows a histogram of the distribution of monthly returns for the U.S. stock market over a 273-month period.

Part (a). Describe the overall shape of the distribution of monthly returns.

Part (b). What is the approximate center of this distribution?

Part (c). Explain why you cannot find the exact value for the minimum return. Between what two values does it lie?

Part (d). A return less than 0 means that stocks lost value in that month. About what percent of all months had returns less than 0?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.

Sign-up for free