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The X axis is labeled using the “scores” of political party order anafranil from india, and because this is a nominal variable cheap anafranil express, they can be arranged in any order purchase anafranil toronto. In the frequency table buy anafranil discount, we see that six people were Republicans, so we draw a bar at a height (frequency) of 6 and so on. Say that the lower graph is from a survey in which we counted the number of partic- ipants having different military ranks (an ordinal variable). Political affiliation Ordinal Variable of 8 Military Rank 7 Party f 6 General 3 5 Colonel 8 f 4 Lieutenant 4 Sergeant 5 3 2 1 0 Sgt. Later we will see bar graphs in other contexts and this same rule always applies: Create a bar graph whenever the X variable is discrete. On other hand, recall that interval and ratio scales are assumed to be continuous:They allow fractional amounts that continue between the whole numbers. Histograms Create a histogram when plotting a frequency distribution containing a small number of different interval or ratio scores. A histogram is similar to a bar graph except that in a histogram adjacent bars touch. For example, say that we measured the number of parking tickets some people received, obtaining the data in Figure 3. Although you can- not have a fraction of a ticket, this ratio variable is theoretically continuous (e. By having no gap between the bars in our graph, we communicate that there are no gaps when measuring this X variable. Polygons Usually, we don’t create a histogram when we have a large number of dif- ferent interval or ratio scores, such as if our participants had from 1 to 50 parking tick- ets. The 50 bars would need to be very skinny, so the graph would be difficult to read. We have no rule for what number of scores is too large, but when a histogram is unwork- able, we create a frequency polygon. Construct a frequency polygon by placing a data point over each score on the X axis at a height corresponding to the appropriate fre- quency. Because each line continues between two adjacent data points, we communicate that our measurements continue between the two scores on the X axis and therefore that this is a continuous variable. Later we will create graphs in other contexts that also involve connecting data points with straight lines. This same rule always applies: Connect adjacent data points with straight lines whenever the X variable is continuous. In this way, we create a complete geometric figure—a polygon—with the X axis as its base. Often in statistics you must a read a polygon to determine a score’s frequency, so be sure you can do this: Locate the score on the X axis and then move upward until you reach the line forming the polygon. To show the number of freshmen, sophomores, and a histogram with a few interval/ratio scores, and a juniors who are members of a fraternity, plot a. To show the number of people preferring chocolate versus females (a nominal variable), create a bar or vanilla ice cream in a sample, plot a. Call it a normal curve or a normal distribution or say that the scores are normally distributed. Because it represents an ideal population, a normal curve is different from the choppy polygon we saw previously. First, the curve is smooth because a population produces so many different scores that the individual data points are too close to- gether for straight lines to connect them. Second, because the curve reflects an infinite number of scores, we can- not label the Y axis with specific frequencies. Simply remember that the higher the curve is above a score, the higher is the score’s frequency. Finally, regardless of how high or low an X score might be, theoretically it might sometimes occur. Therefore, as we read to the left or to the right on the X axis, the frequencies approach—but never reach—a frequency of zero, so the curve approaches but never actually touches the axis. The score with the highest frequency is the middle score between the highest and lowest scores. As we proceed away from the middle score either toward the higher or lower scores, the frequencies at first decrease slightly. Farther from the middle score, however, the frequencies decrease more drastically, with the highest and lowest scores having relatively low frequency. In statistics the scores that are relatively far above and below the middle score of the dis- tribution are called the “extreme” scores. Then, the far left and right portions of a normal curve containing the low-frequency, extreme scores are called the tails of the distribution. The reason the normal curve is important is because it is a very common distribution in psychology and other behavioral sciences: For most of the variables that we study, the scores naturally form a curve similar to this, with most of the scores around the middle score, and with progressively fewer higher or lower scores. Because of this, the normal curve is also very common in our upcoming statistical procedures. Do you see that a score of 15 has a rela- tively low frequency and a score of 45 has the same low frequency? Do you see that there are relatively few scores in the tail above 50 or in the tail below 10? On a normal distribution, the farther a score is from the central score of the distribution, the less frequently the score occurs. A distribution may not match the previous curve exactly, but it can still meet the mathe- matical definition of a normal distribution. Curve A is skinny relative to the ideal because only a few scores around the middle score have a relatively high fre- quency. On the other hand, Curve C is fat relative to the ideal because more scores farther below and above the middle have a high frequency. Because these curves generally have that bell shape, however, for statistical purposes their differences are not critical. Other Common Frequency Polygons Not all data form a normal distribution and then the distribution is called nonnormal. A negatively skewed distribution contains extreme low scores that have a low fre- quency but does not contain low-frequency, extreme high scores. This pattern might be found, for example, by measuring the running speed of professional football players. Most would tend to run at higher speeds, but a relatively few linemen lumber in at the slower speeds. This pattern might be found, for example, if we measured participants’ “reaction time” for recogniz- ing words. Usually, scores will tend to be rather low, but every once in a while a person will “fall asleep at the switch,” requiring a large amount of time and thus producing a high score. Another type of nonnormal distribution is a bimodal distribution, shown in the left- hand side of Figure 3. A bimodal distribution is a symmetrical distribution contain- ing two distinct humps, each reflecting relatively high-frequency scores. High scores scores of each hump is one score that occurs more frequently than the surrounding scores, and technically the center scores have the same frequency. Such a distribution would occur with test scores, for example, if most students scored at 60 or 80, with fewer students failing or scoring in the 70s or 90s. Finally, a third type of distribution is a rectangular distribution, as shown in the right-hand side of Figure 3. There are no discernible tails be- cause the frequencies of all scores are the same. Labeling Frequency Distributions You need to know the names of the previous distributions because descriptive statistics describe the characteristics of data, and one very important characteristic is the shape of the distribution that the data form. Thus, although I might have data containing many different scores, if, for example, I tell you they form a normal distribution, you can mentally envision the distribution and quickly and easily understand what the scores are like: Few scores are very low or very high, with the most common, frequent scores in the middle. Therefore, the first step when examining any data is to identify the shape of the simple frequency distribution that they form. Recognize, however, that data in the real world will never form the perfect shapes that we’ve discussed. Instead, the scores will form a bumpy, rough approximation to the ideal distribution. For example, data never form a perfect normal curve and, at best, only come close to that shape.  