5.2 Interpreting Histograms
Making a statistical graph is not our ultimate goal when we are analyzing data. This just helps us to understand the data. After you have created the graph, you should be able to see its important features. Some of those are described below. 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, which has to do with its peaks and symmetry or asymmetry, center, which tells where the middle value of the data lies, and variability, which basically gives the smallest and largest values of the data. An important kind of deviation is an outlier, an individual value that falls outside the overall pattern.
Look at the histogram below, which is one created from data in section 5.1.
Shape: The distribution has a single peak, which represents states in which less than 5% of adults are Hispanic. Center: Since 37 states are to the left of 10 and only 13 are to the right, the center of the data appears to be somewhere between 5 and 10.
Variability: The span of the data is from about 1 to 42 %, but only six states exceed 20%. We might call New Mexico an outlier, with 42.3%.
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When you describe a distribution, concentrate on the main features. Look for major peaks, not just minor ups and downs, and look for clear outliers, not just the smallest or largest observation. Also, look for rough symmetry or asymmetry. Some variables have distributions which form a heap on one side and the rest of the values stretch out into a long tail on the other side. This trait is known as skewness, and can go in either direction.
A right­skewed distribution is a distribution in which the longer tail of the histogram is on the right side. (This can also be called "positively skewed.") A left­skewed distribution is a distribution in which the longer tail of the histogram is on the left side. (This can also be called "negatively skewed.") 2
A distribution is symmetric if it is not skewed and values are distributed similarly on both sides. (In this case, a vertical line could be superimposed on the histogram and have the left and right sides be approximate mirror images of each other.)
Ex: Tell whether each histogram below is right­skewed, left­skewed, or symmetric.
a) b)
c)
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The histogram below displays the scores of a group of seventh­grade students on the Iowa Test of Basic Skills. Describe the distribution, estimate the center, and give the variability.
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