Business Statistics: Summarizing Data

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Questions and Answers

What is the formula used to decide the number of classes?

k = n

k = n/2

2k ≥ n (correct)

k = √n

What is the purpose of subtracting 1 from the lower limit of the second class?

To get the upper limit of the first class (correct)

To get the number of classes

To get the lower limit of the first class

To get the class width

What is the formula used to obtain the class width?

w = (H - L) / k (correct)

w = (H + L) / k

w = H - L

w = (H - L) / (k - 1)

What type of graph displays the data using contiguous vertical bars of various heights?

Histogram Signup and view all the answers

What type of graph represents the cumulative frequencies for the classes in a frequency distribution?

Cumulative frequency curve (Ogive) Signup and view all the answers

What is the purpose of tallying and recording the number of items in each class?

To construct the frequency distribution Signup and view all the answers

What is the range of values in a class interval called?

Class width Signup and view all the answers

What type of data is typically represented by a histogram?

Quantitative data Signup and view all the answers

What is the purpose of a scatter plot?

To determine the relationship between two variables Signup and view all the answers

What kind of data is best represented by a bar graph?

Categorical data with multiple categories Signup and view all the answers

What is the main feature of a pie chart?

Each sector's area is proportional to the frequency of the category Signup and view all the answers

What is the main purpose of an Ogive plot?

To show the cumulative frequency of a dataset Signup and view all the answers

Which type of graph is best suited for bivariate data?

Scatter plot Signup and view all the answers

What is the advantage of using a pie chart?

It is easy to compare the frequencies of different categories Signup and view all the answers

What type of data is an Ogive plot used for?

Quantitative data with cumulative frequencies Signup and view all the answers

Which type of graph is used to display categorical data with multiple categories?

Bar graph Signup and view all the answers

What is the primary purpose of a frequency distribution table?

To organize raw data into mutually exclusive categories Signup and view all the answers

What is the minimum number of classes recommended for a frequency distribution table?

5 Signup and view all the answers

What is the term for the midpoint between the upper limit of a class and the lower limit of the next class in sequence?

Class boundary Signup and view all the answers

What is the purpose of adjusting the class limits by adding or subtracting 0.5?

To separate classes Signup and view all the answers

What is the difference between the lower and upper class limits called?

Class width Signup and view all the answers

What is the formula to determine the number of classes in a grouped frequency distribution?

2k ≥ n Signup and view all the answers

Why must the classes in a frequency distribution table be mutually exclusive?

So that each observation can be placed into only one class Signup and view all the answers

What happens if there are gaps in a frequency distribution table?

The classes are not continuous Signup and view all the answers

What is the definition of the class midpoint?

The average of the lower and upper class limits Signup and view all the answers

Why must the classes in a frequency distribution table be exhaustive?

So that all observations can be accommodated Signup and view all the answers

How is the class width determined in a grouped frequency distribution?

By dividing the range by the number of classes Signup and view all the answers

What is the starting value of each class called?

Lower limit Signup and view all the answers

What is the purpose of the formula w≥ (H - L) / k?

To determine the class width Signup and view all the answers

What is the definition of the relative frequency?

The proportion of values falling into a specific class Signup and view all the answers

What is the purpose of the cumulative frequency?

To sum the frequency of a class and the frequencies of all classes below it Signup and view all the answers

What is the step in constructing a grouped frequency distribution that involves setting the individual class limits?

Step 3: Set the individual class limits Signup and view all the answers

Study Notes

Summarizing Data

Summarizing data graphically involves organizing raw data into mutually exclusive categories to show the number of observations in each class.

Frequency Distribution Table

A frequency distribution table is a table that organizes raw data into mutually exclusive categories showing the number of observations in each class.
Rules for constructing frequency distribution tables: • The table should have between 5 and 20 classes. • Classes must be mutually exclusive, continuous, and exhaustive. • Classes must be equal in width and size.

Definitions

Class Limit: the starting and ending point of a particular class.
Class Boundary: the midpoint between the upper class limit of a class and the lower class limit of the next class in sequence.
Class Width/Size: the difference between the lower and upper class boundaries of a class interval.
Class Midpoint: a point that divides a class into two equal parts.
Class Frequency (f): the number of observations in each class.
Relative Frequency (RF): the proportion of values falling into that class.
Cumulative Frequency (CF): obtained by summing the frequency of a class and the frequencies of all the classes below it.

Constructing Grouped Frequency Distribution

Steps for constructing grouped frequency distribution:
1. Decide the number of classes using the formula 2k ≥ n, where k is the number of classes and n is the number of observations.
2. Determine the class width using the formula w ≥ (H – L) / k, where H is the highest value and L is the lowest value.
3. Set the individual class limits by starting from the lowest value in the data and adding the width to get the lower limit of the next class.
4. Tally and record the number of items in each class.

Graphs for Quantitative Data

Histogram: a graph that displays the data by using contiguous vertical bars of various heights to represent the frequencies of the classes.
Cumulative Frequency Curve (Ogive): a graph that represents the cumulative frequencies for the classes in a frequency distribution.
Scatter Plot: a graph that shows how one variable is affected by another.

Graphs for Categorical Data

Bar Graph: a graph of vertical or horizontal bars whose heights represent the frequencies of respective categories.
Pie Chart: a circle divided into sectors, where each sector represents a category of data and the area of each sector is proportional to the frequency of the category.

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Description

This quiz covers the basics of summarizing data graphically and frequency distribution tables in business statistics.