Stats: Chapter 2

Scores out of (100) on an easy test where most students did well.

Skewed to the left because of the few who score poorly.of the few who score poorly. nothing

Number of vehicles per household.

Skewed to the right because most households have less than or equal to three cars.less than or equal to three cars.

A recent national census found that the median household income in a certain country was $79,100 and the mean was $75,100. Based on only this​ information, what would you predict about the shape of the​ distribution? Why?

The fact that the mean is less than the median indicates that there are extremely low incomes that are affecting the ​mean, but not the median comma but not the median, suggesting that the shape is skewed to the left.

If you had data for all students in your school on the amount of money spent in the previous year on overnight stays in a​ hospital, probably the median and mode would be 0 but the mean would be positive.

The majority of students will not have stayed overnight in a hospital during the previous​ year, but those who did will spend a positive amount.

BiModal Distribution

When a data set has 2 modes.

The data report total emissions for each country. Describe a situation in which it may be more useful to analyze per capita data. Choose the correct answer below.

A researcher is studying consumer emissions.

Split Stem

First leaf 0-4. Second 5-9.

Unimodal Distribution

When the data set only has 1 mode.

What is the difference between categorical and quantitative​ variables?

A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable.

Median

Middle number

Standard Deviation

1. Work out the mean (average). 2. For each number, subtract the mean and square the result. 3. Work out the mean in the squared differences. 4. Take the square root of that.

Skewed to the Left

A distribution is skewed to the left if the left tail is longer than the right. That​ is, there are a few observations significantly smaller than the others.

Skewed to the Right

A distribution is skewed to the right if the right tail is longer than the left. That​ is, there are a few observations significantly larger than the others.

Continuous

Continuous data are not restricted to defined separate values, but can occupy any value over a continuous range. Between any two continuous data values there may be an infinite number of others. Continuous data are always essentially numeric.

What information can a histogram show that a time plot does not​ provide?

A histogram shows the viewer the number of observations at each level and the shape of the distribution.

What information can a time plot show that a histogram cannot​ provide?

A time plot connects the data points over time to show time trends.

How to find the proportion.

Add all the counts together and divide the count by the total number of counts.

Resistant

Since the median for all three sets is the​ same, the median is resistant.

Range

The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Choose the correct interpretation of the standard deviation below.

The standard deviation represents a typical distance of an observation from the mean.

Is the variable continuous or​ discrete? Why?

is a continuous variable since it has an infinite continuum of possible values.

What is the effect of the​ outlier?

Both the range and standard deviation increase when an outlier is added

For each​ woman, the number of children is a whole​ number, such as 2 or 3. Explain why it makes sense to measure a mean number of children per adult woman​ (which is not a whole​ number) to compare fertility levels.

For discrete data that take only a few​ values, quite different patterns of data can give the same result for the median. The​ mean, however, can take on any numerical​ value, making it a better measure of center in these cases.

Not Resistant

Notice that as the value of the fifth observation​ increases, so does the mean. That​ is, an outlier influences the value of the mean.​ Thus, the mean is not resistant.

Is the​ variable, number of concerts attended​, discrete or​ continuous?

Number of concerts attended is a discrete variable since it has a finite number of possible values.

If 17351 observations shift from 0 to 4 or​ more, how do the mean and median​ change?

The mean increases while the median remains the same.

Compare the​ stem-and-leaf plot from part a to the​ stem-and-leaf plot from part c. Explain how one may be more informative than the other. Choose the correct answer below.

Using split stems in part c more clearly portrays where the data fall. In this​ case, it shows that the distribution of selling amounts may be bimodal whereas the plot from part a indicates that the distribution is unimodal.

Mode

Largest number and most frequent number in a dot plot.

Discrete

Discrete data can only take particular values. There may potentially be an infinite number of those values, but each is distinct and there's no grey area in between. Discrete data can be numeric -- like numbers of apples -- but it can also be categorical -- like red or blue, or male or female, or good or bad.

On a class​ survey, students were asked to estimate the number of times a​ week, on​ average, that they read a daily newspaper.

Discrete, because the value for each person would be a whole number.

Is the variable continuous or​ discrete? Why?

is a discrete variable since it has a finite number of possible values.

Is the variable continuous or​ discrete? Why?

is a discrete variable since it has finite number of possible values.