Formulas to remember

Question 1

Formula for the width of a class in a histogram

Answer 1

(Largest value - Smallest Value) / (Number of Classes)

Question 2

What is the reccomended amount of classes for a histogram?

Answer 2

2^k > n

To determine if our choices are valid, we can also follow the rule of 2 to the k larger than n.

The first value of k that brings it above n is the number of classes we should choose

It is reccomended that it be between 5 and 20

Question 3

What is the difference between Histograms and Bar Charts?

Answer 3

The histogram is specifically for class intervals and numbers that we can add together to create cumulative frequency distributions. These are specific to quantitative data. Earlier, we depicted sleep hours in a histogram.

In contrast, bar charts deal with categories, classes, and labels, such as nominal and ordinal data. Earlier, we depicted student motivation for a major as a bar chart.

Question 4

Histogram

Answer 4

A histogram displays:

Class intervals
Class frequencies

Histograms are appropriate for quantitative data.

Question 5

Bar Chart

Answer 5

A bar chart displays:

Frequencies for a set of categories or classes
Bar charts are better for qualitative data.

Question 6

Ogive

Answer 6

Definition: Graphical representation showing cumulative frequency through class midpoints.

Calculation: Plot cumulative frequency against class midpoints.

Cumulative Nature: Frequency increases cumulatively.

Endpoint: Typically stops at 100% frequency.

Purpose: Alternative data visualization.

Example: First class interval 25-31, midpoint 28, plotted on ogive.

Application: Analyzing cumulative trends in data.

Question 7

Stem and Leaf Plot

Answer 7

Definition: Technique for visualizing data distribution by showing stems (leading digits) and leaves (trailing digits).

Purpose: Provides a snapshot of data distribution, aiding in quick understanding.

Procedure:
Choosing Stem: Select stem (leading digit) based on data range.

Adding Leaves: For each stem, list leaves (trailing digits) in ascending order.

Rounding Data: Sometimes necessary to round data to fit display, particularly when using larger leaf units.

Application: Used in descriptive statistics to illustrate data distribution effectively.

Question 8

Calculating the Median

Answer 8

Calculating the Median

Step 1: Sort Values
Arrange values in ascending or descending order.

Step 2: Verify Odd/Even
Determine if the dataset has an odd or even number of values.

Step 3: Split Dataset
Divide the dataset into two equal halves.

Step 4: Round Up
Round the split position to the nearest integer.

Conclusion: The value at the rounded-up position represents the median.