The ogives shown are based on U.S. Census data and show the...

The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars. (a) How were the percentages shown in graph (ii) computed? (b) How many states have average per capita income less than 37.5 thousand dollars? (c) How many states have average per capita income between 42.5 and 52.5 thousand dollars? (d) What percentage of the states have average per capita income more than 47.5 thousand dollars?

The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars.
(a) How were the percentages shown in graph (ii) computed?
(b) How many states have average per capita income less than 37.5 thousand dollars?
(c) How many states have average per capita income between 42.5 and
52.5 thousand dollars?
(d) What percentage of the states have average per capita income more than
47.5 thousand dollars?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Ogive

An ogive is a graph that represents a cumulative frequency distribution. It plots the cumulative total of the data values, allowing you to see at a glance the proportion of the data that falls below a specific value. This aids in understanding the distribution and locating percentiles in the dataset.

Cumulative Frequency Distribution

A cumulative frequency distribution is a way to summarize data by progressively adding the frequencies of the data points or intervals. It shows how many observations fall below each successive value, providing a cumulative count that is critical for determining medians, quartiles, and other percentiles.

Percentage Calculation

Calculating percentages in data analysis involves dividing the count of observations in a specific category by the total number of observations and then multiplying by 100. This concept is essential for converting raw frequencies into relative terms, which facilitates comparisons across different data segments.

Interpreting Graphical Data

Interpreting graphical data, such as that shown in an ogive, involves reading the cumulative values at specific data points or intervals. This skill allows one to estimate the number of observations that lie below, within, or above certain thresholds, which is crucial for answering questions about ranges and proportions in a dataset.

Transcript

Please give Ace some feedback