Data from the U.S. Census Bureau provides the population by state in millions of people (The Wor

Data from the U.S. Census Bureau provides the population by...

Key Concepts

Descriptive Data Analysis

Descriptive data analysis involves summarizing and interpreting data characteristics through methods such as tabulation, graphical display, and computation of statistics like skewness. This analysis helps in drawing observations about the underlying patterns and properties of the dataset, thereby allowing insights into variations and trends among data points.

Skewness

Skewness is a measure of the asymmetry of a data distribution around its mean. It indicates whether the data values tend to have a longer tail on one side (positive or negative skew), which can affect the interpretation of the central value and signal the presence of outliers or a non-normal distribution.

Percent Frequency Distribution

A percent frequency distribution converts the raw counts of observations in each interval into percentages of the total data. This form of distribution provides a clearer picture of the relative proportion of data in each class, making it easier to compare different segments of the data set.

Frequency Distribution

A frequency distribution organizes data into intervals (or classes) and records the number of observations that fall into each interval. This helps in understanding the distribution of data points across different ranges and is fundamental in descriptive statistics for summarizing how data is spread out.

Histogram

A histogram is a graphical representation of the frequency distribution where data is divided into intervals or bins, and the frequencies (or percent frequencies) are depicted by the heights of bars. This visual tool is essential for identifying patterns such as distribution shape, central tendency, and spread.

Transcript

00:01 Hey everyone, today we're solving problem number 44 from chapter 2 to text book.

00:05 Let's get started.

00:06 In part a, we're asked to find the frequency and percent frequency.

00:10 And this data is all about the population of 50 different cities in millions.

00:18 So with frequency, we know that the total has to be 50 by zero because that is our sample size, 50 different cities.

00:28 And then with percent frequency, we know that the percent's all have to add up to 100%, because 100 % means you have a whole part in a whole hole.

00:41 So essentially, that means you have the whole.

00:44 So there's no part to whole ratio.

00:47 It's just the whole itself.

00:49 So let's get started.

00:51 So from 0 to 2 .4 million, i see 17 different cities.

00:57 Again, you can count off.

00:58 17 different cities have this population.

01:00 Then from 2 .5 to 4 .9 million, i see 12 different cities.

01:07 Then from 5 .0 to 7 .4 million people, i see nine different cities.

01:14 Then i see four, then three, and you just keep going down and down.

01:19 One thing to note about this is that they tell you to make the scale by increments of every 2 .5 million people.

01:26 So bear that in mind while you're doing this.

01:29 And i see one, one, zero, one, between 22 and a half and 24 .9 million.

01:42 Then i have four different zeros.

01:47 So nothing between 25 and essentially 35 million.

01:51 And then from 35 million to 37 .4 million, i have one city.

01:57 So those are my frequencies filled out in the table.

02:01 Now to find percent frequency, what you're going to notice is that for your total of 50, to get to your total of 100, you need to multiply by 2.

02:09 So you're going to multiply each of your frequencies by 2.

02:12 So 17 times 2 is going to be 34%.

02:17 Between 0 .2 .4 million.

02:20 24%, because 12 times 2 is 24.

02:23 And that's going to be between 2 .5 and 4 .9 million.

02:27 Then between 5 and 7 .4 million, you're going to have 13%.

02:32 Then between 7 .5 and 9 .9 million, we're going to have 13%.

02:37 Then between 7 .5 and 9 .9 million, we're going to have.

02:41 Have 8 different cities, i mean 8%, sorry, 6%, 2%, 2%, 2%, 2%, obviously 0 times 2 is 0, because 0 times anything is 0, 2 % there, 4 0, and then between 35 million people and 37 .4 million people, that will account for 2%.

03:16 If you wanted to check, you could add these all up and they should equal 100.

03:20 And in fact, they do.

03:21 So moving on to kind of the second part of the first part, we're asked to draw a histogram of the frequencies.

03:30 So let's get started.

03:33 An important thing about this histogram is that you need to make sure that your scaling is correct and that you have equal size widths of your bars.

03:45 So between 0 and 2 .4 million, which is about halfway there, i have 17, a frequency 17.

03:55 So i have between 15 and 20.

03:56 This is obviously 17 and a half because i went up like increments of 2 .5.

04:00 So 17 is probably around there.

04:07 Again, we're just trying our best to make the right and shade it in as best as you can.

04:19 Obviously with the pen and paper, shading all this in is really easy.

04:23 And i'm going to write 17...