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Chapter 2: Problem 1

Why do we need to group data in the form of a frequency table? Explain briefly.

Short Answer

Expert verified
Frequency tables are needed to group data because they simplify complex data sets, making them understandable and manageable. They facilitate the comparison of data, identification of patterns and trends, data interpretation, and decision-making, which are vital in statistical data analysis.

Step by step solution

01

Understand data grouping and frequency tables

Data grouping refers to the process of categorizing data into different groups or classes according to certain criteria. Frequency tables are a tool used in statistical analysis to summarize a set of data. It is a way of showing how frequently certain classes or ranges of values occur in the given data set.
02

Identify benefits of frequency tables

Frequency tables offer several benefits. They simplify complex data sets making them more understandable, they facilitate the analysis of large data sets, and they help in identifying patterns and trends within the data.
03

Explain need of frequency tables

In data analysis, it's essential to simplify and summarize the data in order to understand it better. A frequency table does just that, making it easier to compare data, identify patterns, analyze trends, draw interpretations, and make informed decisions. This necessitates grouping data in the form of frequency tables.

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Most popular questions from this chapter

The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student. \(\begin{array}{llllllllll}32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61\end{array}\) Create a dotplot for these data.

The following data give the political party of each of the first 30 U.S. presidents. In the data, D stands for Democrat, DR for Democratic Republican, \(\mathrm{F}\) for Federalist, \(\mathrm{R}\) for Republican, and \(\mathrm{W}\) for Whig. $$ \begin{array}{llllllllll} \text { F } & \text { F } & \text { DR } & \text { DR } & \text { DR } & \text { DR } & \text { D } & \text { D } & \text { W } & \text { W } \\ \text { D } & \text { W } & \text { W } & \text { D } & \text { D } & \text { R } & \text { D } & \text { R } & \text { R } & \text { R } \\ \text { R } & \text { D } & \text { R } & \text { D } & \text { R } & \text { R } & \text { R } & \text { D } & \text { R } & \text { R } \end{array} $$ a. Prepare a frequency distribution table for these data. b. Calculate the relative frequency and percentage distributions. c. Draw a bar graph for the relative frequency distribution and a pie chart for the percentage distribution. d. Make a Pareto chart for the frequency distribution. e. What percentage of these presidents were Whigs?

The following data give the number of orders received for a sample of 30 hours at the Timesaver Mail Order Company. \(\begin{array}{llllllllll}34 & 44 & 31 & 52 & 41 & 47 & 38 & 35 & 32 & 39 \\\ 28 & 24 & 46 & 41 & 49 & 53 & 57 & 33 & 27 & 37 \\ 30 & 27 & 45 & 38 & 34 & 46 & 36 & 30 & 47 & 50\end{array}\) Create a dotplot for these data.

The following data give the number of orders received for a sample of 30 hours at the Timesaver Mail Order Company. $$ \begin{array}{llllllllll} 34 & 44 & 31 & 52 & 41 & 47 & 38 & 35 & 32 & 39 \\ 28 & 24 & 46 & 41 & 49 & 53 & 57 & 33 & 27 & 37 \\ 30 & 27 & 45 & 38 & 34 & 46 & 36 & 30 & 47 & 50 \end{array} $$ a. Construct a frequency distribution table. Take 23 as the lower limit of the first class and 7 as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. For what percentage of the hours in this sample was the numher of orders more than 36 ? d. Prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions.

The following data give the results of a sample survey. The letters \(\mathrm{Y}, \mathrm{N}\), and \(\mathrm{D}\) represent the three categories. $$ \begin{array}{llllllllll} \mathrm{D} & \mathrm{N} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{Y} & \mathrm{D} & \mathrm{Y} \\ \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{N} & \mathrm{Y} \\ \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{D} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} \\ \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{N} & \mathrm{D} & \mathrm{Y} \end{array} $$ a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of the elements in this sample belong to category Y? d. What percentage of the elements in this sample belong to. category \(\mathrm{N}\) or \(\mathrm{D}\) ? e. Draw a pie chart for the percentage distribution. f. Make a Pareto chart for the percentage distribution.
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