statistics sheet

GENERAL RULES FOR FORMING FREQUENCY DISTRIBUTIONS

1. Determine the largest and smallest numbers in the raw data and thus find the range (the difference between the largest and smallest numbers).
2. Divide the range into a convenient number of class intervals having the same size. If this is not feasible, use class intervals of different sizes or open class intervals. The number of class intervals is usually taken between 5 and 20, depending on the data. Class intervals are also chosen so that the class marks (or midpoints) coincide with the actually observed data. This tends to lessen the so-called grouping error involved in further mathematical analysis. However, the class boundaries should not coincide with the actually observed data.
3. Determine the number of observations falling into each class interval; that is. find the class frequencies. This is best done by using a tally, or score sheet.

HISTOGRAMS AND FREQUENCY POLYGONS

Histograms and frequency polygons are two graphic representations of frequency distributions.

1. A histogram, or frequency histogram, consists of a set of rectangles having (a) bases on a horizontal axis (the x axis), with centers at the class marks and lengths equal to the class interval sizes, and (b) areas proportional to the class frequencies If the class intervals all have equal size, the heights of the rectangles arc proportional to the class frequencies, and it is then customary to take the heights numerically equal to the class frequencies. If the class intervals do not have equal size, these heights must be adjusted.
2. A frequency polygon is a line graph of the class frequency plotted against the class mark. It can be obtained by connecting the midpoints of the tops of the rectangles in the histogram.

The histogram and frequency polygon corresponding to the frequency distribution of heights in Table 2 are shown on the same set of axes in Fig. 1. It is customary to add the extensions PQand RS to the next-lower and -higher class marks, which have a corresponding class frequency of zero. In such case the sum of the areas of the rectangles in the histogram equals the total area bounded by the frequency polygon and the X axis.