Statistics 1A Chapter 1.2

modes / unimodal

(major peaks) is another aspect of the overall shape A distribution with one major peak is called unimodal.

Make a Stemplot

1. Separate each observation into a stem consisting of all but the final (rightmost) digit and a leaf, the final digit. Stems may have as many digits as needed, but each leaf contains only a single digit. 2. Write the stem in a vertical column with the smallest a the top, and draw a vertical line at the right of this column. 3. Write each leaf in the row to the right of its stem, in increasing order out from the stem.

Difference Bar Graph / Histogram

A histogram shows the distribution of counts or percents among the values of a single variable. A barograph compared the counts of different items. The horizontal axis of a bar graph need not to have any measurement scale but identifies the items being compared. Draw bar graphs with blank spaces between the bars to separate the items being compared. Draw histograms with no space to indicate that all values of the variable are covered.

Stemplots & Histograms

Display the distribution of a quantitative variables. Stemplots separate each observation into a stem and a one-digit leaf. It gives a quick picture of the shape of a distribution while including the actual numerical values in the graph. Stemplots work best for small numbers of observations that are greater than 0. Histograms do not have these limitations. Histograms plot the frequencies (counts) or the percents of equal width classes of values. A histogram breaks the range of values of a variable into classes and displays only the count or percent of the observation that fall into each class. You can choose any convenient number of classes , but you should always choose classes of equal width. Use histograms of percents for comparing several distributions that have different numbers of observation. The choice of classes affects the histogram.

Bar graphs & pie charts

Display the distributions of categorical variables. These graphs use the counts or percents of the categories. To make a pie chart, you must include all the categories that make up a whole. This constraint makes Bar graphs more flexible.

Examining a distribution

In any graph of data, look for the overall pattern and for striking deviations from that pattern. You can describe the overall pattern of a distribution by its shape, center & spread. An important kind of deviation is an outlier, an individual value that falls outside the overall pattern.

Outliers

Observations that lie outside the overall pattern of a distribution. Lecture: What is an outlier? An outlier is a value that appears to be unusually large or small, given the rest of the data. Look around the room. Would a 175cm tall person be unusual? A 100cm tall person? › Why are outliers important? An outlier may represent a sample from outside the population of interest Outliers have a large effect on many statistics - like mean, standard deviation Outliers may represent errors in the data - example: a height of 100cm What to do about outliers: remove them examine whether the outliers signal a problem with your sampling obtain more data (maybe they aren't really outliers)

Explanatory data analysis

Statistical tools and ideas help us examine data to describe their main features.

Tails

The extreme values of a distribution are in the tails of the distribution. The high values are in the upper, or right, tail, and the low values are in the lower, or left tail.

shape, center, spread, deviations

When examining a distribution look for ____, _____ and _____ and for clear __________ from the overall shape.

time plot

When observations on a variable are taken over time, make a ____ ____ that graphs time horizontally and the values of the variable vertically. A time plot can reveal changes over time. Always put the time on the horizontal scale of your plot and the variable you are measuring on the vertical scale.

Distribution of a categorical variable

lists categories and gives either the count or the percent of cases that fall into each category.

Simple shapes of deviations

skewed or symmetric - it is symmetric if the values smaller and larger than its midpoint are mirror images of each other. It is skewed to the right, if the right tail (larger values) is much longer than the left tail (smaller values).