/*! 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} Problem 47 Use the following information to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 47

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following: median \(=\)____

Short Answer

Expert verified
The median number of cars sold is 4 cars.

Step by step solution

01

Organize the Data

List the number of sales each car salesperson has reported in ascending order. Count the frequency of each sales number: 3 (14 times), 4 (19 times), 5 (12 times), 6 (9 times), 7 (11 times). The total number of data points is 65.
02

Identify Median Position

Find the median position using the formula \( \text{median position} = \frac{n+1}{2} \). Here, \( n = 65 \), so \( \text{median position} = \frac{65+1}{2} = 33 \). The 33rd data point is the median.
03

Locate the Median Value

Count the data points to find the value at the 33rd position. The sequence starts with 14 entries of 3, followed by 19 entries of 4. Therefore, the 33rd position falls in the sales of 4 cars (14 for 3 + 19 for 4 = 33).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency Distribution
Understanding frequency distribution is essential in identifying how often data points occur within a data set. In this case, car salespersons were surveyed to determine how many cars they sell in a week. Each salesperson had a specific number of cars sold, organized in a frequency distribution based on their responses. A frequency distribution helps in visualizing data to see the commonality and rarity of data points. For example:
  • 14 salespeople reported selling 3 cars.
  • 19 salespeople reported selling 4 cars.
  • 12 salespeople reported selling 5 cars.
  • 9 salespeople reported selling 6 cars.
  • 11 salespeople reported selling 7 cars.
This approach simplifies identifying trends among salespeople. The frequency distribution serves as a cornerstone in statistical analysis, helping to organize data for deeper insights.
Data Organization
Data organization involves arranging data systematically so that it is easier to analyze and interpret. The first step in solving the median calculation problem was to list the sales data in ascending order. By organizing the data according to the number of cars sold, we can easily apply further statistical methods. Data organization requires paying attention to details such as:
  • Arranging numbers in numerical order, from smallest to largest
  • Counting the frequency of each data point
  • Ensuring that every data point is accounted for and accurately displayed
In our example, this meant listing sales frequencies starting with the amount that occurred most often and organizing them sequentially. Proper data organization is essential for ensuring accuracy when performing statistical calculations like finding the median.
Statistical Analysis
Statistical analysis involves breaking down data to understand its various components and making inferences. In this scenario, using the data on car sales among salespeople, we performed statistical analysis to find the median number of sales.The steps included:
  • Identifying the total number of salespeople surveyed (65 in total)
  • Calculating the median position using the formula \( \frac{n + 1}{2} \), where \ n \ is the total number of data points
  • Determining the sales number at that median position
This statistical approach helped us to derive a single value representing the central tendency of the data set, offering a clear insight into the average sales performance.
Central Tendency
Central tendency refers to the measure that identifies the center of a data set, with the median being a key indicator. The median is the middle value that divides the data into two equal parts and provides an understanding of the data's central point.To identify the median:
  • First, the data was sorted in order, which is vital for accurate calculation.
  • The formula \( \text{median position} = \frac{n + 1}{2}\) helped locate the exact median position.
  • In the sales data, this led us to determining the median was the 33rd data point.
The median in this example was determined to be 4 cars sold, which means that half of the salespeople sold fewer than 4 cars and the other half sold more. Understanding central tendency, and specifically the median, provides a simple way to summarize a large amount of data with a single value.

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

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Construct a box plot below. Use a ruler to measure and scale accurately.

\text鈥� # Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows: $$\begin{array}{|l|l|}\hline \\# \text { of movies } & {\text { Frequency }} \\\ \hline 0 & {5} \\ \hline 1 & {9} \\ \hline 2 & {6} \\ \hline 3 & {4} \\\ \hline 4 & {1} \\ \hline\end{array}$$ a. Find the sample mean \(\overline{x}\) . b. Find the approximate sample standard deviation, s.

Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles. 29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150 Find the value that is one standard deviation below the mean.

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976鈥�1977 through 2004鈥�2005. \(\bullet \mu=1000 \mathrm{FTES}\) \(\bullet\) median \(=1,014 \mathrm{FTES}\) \(\bullet \quad \sigma=474 \mathrm{FTES}\) \(\cdot\) first quartile \(=528.5\) FTES \(\cdot\) third quartile \(=1,447.5\) FTES \(\cdot n=29\) years How many standard deviations away from the mean is the median?

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let \(X=\) the number of pairs of sneakers owned.The results are as follows: $$\begin{array}{|l|l|}\hline X & {\text { Frequency }} \\ \hline 1 & {2} \\\ \hline 2 & {5} \\ \hline 3 & {8} \\ \hline 4 & {12} \\ \hline 5 & {12} \\\ \hline 6 & {0} \\ \hline 7 & {1} \\ \hline\end{array}$$ a. Find the sample mean \(\overline{x}\) b. Find the sample standard deviation, s c. Construct a histogram of the data. d. Complete the columns of the chart. e. Find the first quartile. f. Find the median. g. Find the third quartile. h. Construct a box plot of the data. i. What percent of the students owned at least five pairs? j. Find the \(40^{\text { th }}\) percentile. k. Find the \(90^{\text { th }}\) percentile. I. Construct a line graph of the data m. Construct a stemplot of the data
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.