Ch 2 notes

BELL CURVE

bell curve, which is technically known as a "normal distribution." ("Normal" has a special meaning in statistics and always refers to bell-curve shaped distributions.) A normal distribution is curved, with a single hump or mode in the middle, and symmetrical tails,

A distribution with two distinct peaks can be described as...

bimodal

MULTIMODAL

distribution: A distribution can have more than two modes or peaks, in which case it is sometimes called multimodal, although it may be more accurate to say that the distribution doesn't really have any mode at all. Figure 2.17 shows an example of a multimodal distribution. Just like with bimodal distributions, a multimodal distribution can often result from having multiple normal distributions that got combined, as you can see

A normal distribution has a value of skewness that is _____.

near zero

A distribution such as income that has most of the people at the bottom or middle but a few people with extremely high scores, is referred to as...

positivley skewed

A histogram is appropriate when the data are...

quantitative

Univariate

"Uni" is from the Latin unus for "one," as in unicycle (one wheel) or unicorn (one horn). Univariate means one variable; that is, a graph or analysis of one variable at a time. It is usually contrasted with bivariate (two variables at a time) or multivariate (many variables at a time).

PLATYKURTIC

"flat bulge." Think of the flat-tailed platypus of a flat-topped plateau. This kind of distribution can happen when you have "censored" values, which means that scores can't go above or below a particular value. As a result, it tends to have very few outliers. The value of kurtosis for a platykurtic is negative.

bar charts

Bar charts show the number of people (or other observational units) in several different categories by using linear measurements. They can also be used to show means and other summary statistics on quantitative variables. In Excel, a bar chart is horizontal, with the bars going from left to right; the vertical version of a bar chart is called a column chart in Excel. Most people and programs, however, use the term bar chart for both.

Frequency.

Frequency means how often a particular category or score appears in a data set. When used by itself, frequency means that the count, as when you count something starting at 1. However, relative frequency means how often the category or score appears as a percentage or proportion of the total set of scores.

MODE

In statistics, the mode of a distribution is the most frequently occurring score. In a histogram, this shows up as the highest point or hump of the distribution.

quantitative

Interval and ratio variables are quantitative in that they actually measure the distance between scores in consistently sized units, such as number of people, seconds elapsed, or test points. They indicate the size of the difference between two scores.

NEGATIVLEY SKEWED

a distribution may have the extreme scores on the low end, which is called negatively skewedvi or left skewed, again, because that's where the unusual scores are. (LEFT SKEWED) WHEN THE OUTLIERS ARE ON THE LEFT SIDE.

Which type of chart would be most appropriate for a nominal variable?

bar graph

positive skewed

bars are high on the left. .... on the right there is no bars. its skewed .

describe a histogram

bars are touching.

describe a box plot

the one with the interquartiles and the boxes and the outliers that are dots

What is the frequency of 4 in the following data set? 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5

3

Distribution.

A distribution is an organized summary of the data that shows how often each category or score appears. Two common methods for depicting distributions are frequency distribution tables and frequency distribution charts. A frequency distribution table consists of columns and rows of numbers, whereas a frequency distribution chart is a graph like a bar chart or histogram.

categorical

Nominal and ordinal variables are categorical variables in that they do not measure the distance between scores. Instead, they simply indicate that the categories or scores are different.

BIMODAL

On the other hand, a distribution could have two pronounced peaks or humps, in which case it is called bimodal, as in "two modes." Figure 2.15shows an example of a bimodal distribution.

pie charts

Pie charts show the proportion of people (or other observational units) in several different categories by using angular measurements. Pie charts can be created for categorical variables: that is, nominal and ordinal variables. Although pie charts are common, there are several reasons not to use them, which will be discussed below.

histogram

The word "histogram" is derived from the Greek words istos or mast (as in the mast of a sailing ship) and gramma or writing; that is, a histogram is a chart of vertical lines or bars like the masts

POSITIVLEY SKEWED

This is called a positively skewedv distribution, or skewed right, because that's where the extreme scores are (SKEWED RIGHT) WHEN THE OUTLIERS ARE ON THE RIGHT SIDE.

SKEWNESS

This kind of distribution often happens with things relating to money, such as income, where most people earn a small or moderate amount of money each year but a smaller number of people earn an enormous amount.

PREDICTOR VARIABLE

histograms can be used for a simple kind of prediction, where the predictor variable is the one listed across the bottom and the thing being predicted is, for example, the probability of falling into a certain score grouping, which is given by the height of the bar for that score on the X variable, as will be seen below.They also make it very easy to describe the shape of a distribution. Finally, histograms can be used for a simple kind of prediction, where the predictor variable is the one listed across the bottom and the thing being predicted is, for example, the probability of falling into a certain score grouping, which is given by the height of the bar for that score on the X variable, as will be seen below.

A score's frequency is determined by...

how often it occurs in the data set.

UNIFORM DISTRIBUTION

if every score in a distribution is equally likely, which often happens with random variables, then you can have a uniform distribution, which is essentially flat across the top (platykurtic)

LEPTOKURTIC

is narrow and pointed, with long tails, compared to the normal distribution, as "leptokurtic" means "narrow/thin bulge." Think of the long tails of "leaping" kangaroos or a cliff that a skydiver can leap from. Leptokurtic distributions have very little central variation but lots of outliers, which is probably the most important thing about these distributions. Leptokurtic distributions have positive values for kurtosis.

One visual difference between a bar chart and a histogram is that in a histogram...

the adjacent bars touch but in a bar chart they are separate.

KURTOSIS

which means "bulging." Kurtosis has to do with how flat or pointed the distribution is compared to a normal (i.e., bell curve) distribution. In practical terms, the thing that most influences kurtosis is the presence of outliers, as outliers will give the distribution unusually long tails. This has the effect of making the middle part look relatively narrow and pointed.

U-SHAPED DISTRIBUTION

you could have something that is essentially the opposite of a normal distribution, called a U-shaped distribution, because it's high on the ends and low in the middle, like the letter "U." This type of distribution is most likely to occur when there are minimum and maximum values that limit the possible range of score (