Traveling to work How long do people travel each day to get...

Name: Problem 53, Chapter 1: The Practice of Statistics for AP
Uploaded: 2020-11-10T20:43:02-08:00
Duration: 4 min
Channel: Sheryl Ezze

Traveling to work How long do people travel each day to get to work? The following table gives the average travel times to work (in minutes) for workers in each state and the District of Columbia who are at least 16 years old and don’t work at home.30 (a) Make a histogram of the travel times using classes of width 2 minutes, starting at 14 minutes. That is, the first class is 14 to 16 minutes, the second is 16 to 18 minutes, and so on. (b) The shape of the distribution is a bit irregular. Is it closer to symmetric or skewed? About where is the center of the data? What is the spread in terms of the smallest and largest values? Are there any outliers?

Traveling to work How long do people travel each day to get to work? The following table gives the average travel times to work (in minutes) for workers in each state and the District of Columbia who are at least 16 years old and don’t work at home.30
(a) Make a histogram of the travel times using classes of width 2 minutes, starting at 14 minutes. That is, the first class is 14 to 16 minutes, the second is 16 to 18 minutes, and so on.
(b) The shape of the distribution is a bit irregular. Is it closer to symmetric or skewed? About where is the center of the data? What is the spread in terms of the smallest and largest values? Are there any outliers?

Key Concepts

Histogram

A histogram is a graphical representation used to display the distribution of a dataset by grouping data into predetermined intervals (bins). It helps in visualizing the frequency of data points within each range, making it easier to see patterns, such as clusters or gaps in the data.

Bin Width and Class Intervals

Bin width refers to the size of each interval in the histogram, and class intervals are the consecutive intervals that cover the range of the data. Choosing an appropriate bin width is essential, as it affects the visibility of the underlying distribution pattern; too wide a bin may hide important details, while too narrow a bin may create a noisy graph.

Skewness

Skewness describes the degree of asymmetry in a distribution. A symmetric distribution has an even balance on both sides of the central value, whereas a skewed distribution exhibits a longer tail on one side. Recognizing skewness helps in understanding whether the data leans towards higher or lower values.

Measures of Center

Measures of center, such as the median or mean, summarize the central point of a dataset. This value provides a useful summary of a large dataset by indicating where most data values are clustered, which is particularly helpful when the data is distributed unevenly.

Measures of Spread

Measures of spread include indicators like the range (difference between the smallest and largest values) and other dispersion metrics. These measures provide insight into how spread out the data values are, which is essential for understanding the overall variability in a dataset.

Outliers

Outliers are data points that fall significantly outside the overall pattern of the dataset. They can result from variability in measurement or errors, and identifying them is important because they can have a substantial impact on statistical analyses and may indicate interesting anomalies in the data.

Transcript

00:01 So we want to draw a histogram of the data that's listed here.

00:04 And so remember, the histogram has to have some numerical values listed down, which we have the number of minutes of travel time on this horizontal axis.

00:16 And then we're going to have our frequency along this.

00:19 And i'm just going to write the word frequency right here.

00:22 So this is going to be a histogram.

00:25 And our data must be numerical in order to grab a histogram.

00:30 Be a quote bar graph, but we have to have our variable being numerical.

00:35 And so we wanted our classes to all be two minutes wide.

00:38 And so i've already set this up so i can start to grab.

00:41 I also made tick marks.

00:43 I went through and i had 14, 16, and i put the left end of the class, 18, 20, 22, 24, 26, 28, and 30 to 32 is my last class.

00:58 And i basically went through the data.

01:00 And i made tick marks.

01:02 And here will be the frequency that i got from my particular setting.