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# Histogram

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### Histogram

1. 1. COLLEGE OF MANAGEMENT 1
2. 2. “MATHS” TOPIC:- NUMBER OF MEMBERS IN A FAMILY TO:- PROF. 2
3. 3. INDEX SR.NO. TOPICS PAGE NO. 1. BIVARIATE FREQUENCY 4 2. HISTOGRAM 5 3. FREQUENCY POLYGON 6 4. PIE CHART 7 PRESENTED BY:- 3
4. 4. NISHIT ROHIT RUCHITA VINAY VARUN ANISH 4
5. 5. BIVARIATE FREQUENCY "Bivariate" means you will have two variables. Each question in a survey would be considered a variable, so a bivariate analysis could involve two questions from a survey. "Frequency" means you will be counting something, for instance the number of people who give a specific answer to a particular question. For a bivariate frequency distribution you could count the number who gave a specific answer to one question and a specific question to a second question. 5
6. 6. HISTOGRAM In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories. A histogram differs from a bar chart in that it is the area of the bar that denotes the value, not the height, a crucial distinction when the categories are not of uniform width (Lancaster, 1974). The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent. The word histogram is derived from Greek: histos anything set upright' (as the masts of a ship, the bar of a loom, or the vertical bars of a histogram); gramma 'drawing, record, and writing’. The histogram is one of the seven basic tools of quality control, which also include the Pareto chart, check sheet, control chart, cause-and-effect diagram, flowchart, and scatter diagram. A generalization of the histogram is kernel smoothing techniques. This will construct a very smooth probability density function from the supplied data. An example histogram of the heights of 31 Black Cherry trees. 6
7. 7. FREQUENCY POLYGONS Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful in comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions. To create a frequency polygon, start just as for histograms, by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the middle of each class interval at the height corresponding to its frequency. Finally, connect the points. You should include one class interval below the lowest value in your data and one above the highest value. The graph will then touch the X-axis on both sides. 7
8. 8. PIE CHART The following few paragraphs tell you a bit about Pie Charts. A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating relative magnitudes or frequencies or percents. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sectors create a full disk. It is named for its resemblance to a pie which has been sliced. While the pie chart is perhaps the most ubiquitous statistical chart in the business world and the mass media, it is rarely used in scientific or technical publications. It is one of the most widely criticized charts, and many statisticians recommend to avoid its use altogether, pointing out in particular that it is difficult to compare different sections of a given pie chart, or to compare data across different pie charts. Pie charts can be an effective way of displaying information in some cases, in particular if the intent is to compare the size of a slice with the whole pie, rather than comparing the slices among them. Pie charts work particularly well when the slices represent 25 or 50% of the data, but in general, other plots such as the bar chart or the dot plot, or non-graphical methods such as tables, may be more adapted for representing information. The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801. Pie chart of populations of English native speakers 8