Graphical Representation of Data, Slides of Statistics

Download Graphical Representation of Data and more Slides Statistics in PDF only on Docsity! TYPES OF CHARTS AND GRAPH IN STATISTICS Exerquises pe mutt re Why graph and charts? Advantages: - apicture is worth a thousand words - make data simple and intelligible - great memorizing effects universal utility * save time and labour - make comparison easy - attractive and impressive Disadvantages: * numeric detail offered by a table is lost * additional relationships within the data is not known * formatting charts needs more time than tabulation Definition of Bar Graph QA Bar Graph is a chart that uses either horizontal or vertical bars to show comparisons between categories Classification of Bar Charts Number of cars sold in a week . Bite Advantages of Bar chart Represents 4 Black individually 12 * show each data category in a frequency separate and No. of cars sold 6 distinct values. ° distribution : * display relative numbers or proportions of Ye multiple categories IS o . : : Colour of cars * summarize a large data set in visual form | * estimate key values at a glance x * be easily understood due to widespread use in "Sifows the business and the media specific categories being compared. Disadvantages of Bar graph . . . Years 1989 1990 1991 1992 1993 * require additional explanation pratt a * be easily manipulated to yield false $$) impressions Simple Bar Chart nm a * fail to reveal key assumptions, causes, effects, or patterns fe 5S Profit (million $) = ow s8 8 ah 1989 1990 1991 1992 1993 Years 2° « Letus take a large set of numbers :- 24, 17,14, 22, 25, 26, 38, 42, 47, 24, 12, 28, 19, EXAMPLE GRAPH CLASS IINTERVAL 20-30, 30-40 40-50 50-60 PRICE RANGE OF PENS) FREQUENC FREQUENCY(NUMBE | 15 20 30 25 R OF PENS) EXAMPLE of Nek oo Frequency Polygon * frequency polygon: graph that uses lines that connect points plotted for the frequencies at the midpoints of the classes; frequencies are represented by the heights of the points * To construct a frequency polygon: — Find the midpoints of each class — Draw the x and y axes. Label the x-axis with the midpoint of each class then use a suitable scale for the frequencies on the y- axis. — Using the midpoints for the x values and the frequencies asthe y values, plot the points. — Connect adjacent points with line segments. Draw a line back to the x-axis at the beginning and end of the graph (where the next midpoints would be located) Frequency Polygon Example A frequency polygonfor 642psychology test scores shown in Figure was constructed from the frequencytable . Frequency Distribution of Psychology Test Scores. Ds 0 0 3 3 10 13, 53 66 107, 173 147, 320 130, 450 78 528 59 587, 36 623 11 634 6 640 1 641 1 642 0 642 efela * ogive: graph that represents the cumulative frequencies for the classes in a frequency distribution * To construct an ogive: — Find the cumulative frequency for each class — Draw the x and y axes. Label the x-axis with the class boundaries. Label the y-axis with an appropriate frequency ency numbers-yields uneven intervals or classes — Plot the cumulative frequency at each upper class boundary — Starting with the first upper class boundary, connect adjacent points with line segments. Extend the graph to the first lower class boundary on the x-axis Constructing Statistical Graphs- ene Draw and label the x and y-axes Choose a_ suitable scale for the frequencies or cumulative frequencies, and label it on the y- axis. Represent the class boundaries for the histogram or ogive, or the midpoint for the frequency polygon, on the x-axis. Plot the points and then draw the bars or lines. =e laa}e)(= The following data consists of weights, in kilograms, of 20 people: 50, 65,75, 80, 85, 85, 86, 86, 87,87, 87, 90, 92, 98, 105. Placing this data into a stem and leaf plot helps us organise and analyse and group our data better. Thisis not anecessary step. Step 4:-G! dat the tab. Tally Frequency Cumulativ Frequenc y 40<weights<50 IS0<weights<60 |60<weights<70 (70<weights<80 \80<weights<90 \90<weights<100) Step 5: Draw your graph * The first coordinate in the plot always starts at a + value of 0 + The second coordinate is at the end of the first interval. + The third coordinate is at the end of the second interval and sc Weights Ogive eS-en-6360 qrsecanyn Definition of Pie-Chart « Apie chart (also called a Pie Graph or Circle Graph) makes use of sectors in acircle. The angle of a sectoris proportional to the frequency of the data. « Apie chartis a good way of displaying data when you want to show how something is shared or divided. Advantages + Easy to read. * Visually appealing. Disadvantages * They are difficult to draw + Icons must be of consistent size. + Best for only 2-6 categories. + Very simplistic Skewness of data set box plot can be found Box plots (also called box-and-whisker plots or box- whisker plots) give a good graphical image of the concentration of the data. They also show how far the extreme values are from most of the data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them. Step. 1 — Order Numbers 12, 13,5, 8, 9, 20, 16, 14, 14, 6, 9, 12, 12 1. Order the set of numbers from least to greatest 5, G56, 9; 9, 12; 12; 12, 13; 144 14, 16,20 Step 2 — Find the Median 5, 6, 8, 9, 9, 12, 12, 12, 13, 14, 14, 16, 20 Median 12 2. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median? Step 3 — Upper & Lower Quartiles 5, 6, 8,9, 9, 12, 12, 12, 13, 14,/14, 16, 20 lower median upper:median 8.5 Median 14 12 3. Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they? Step 4 — Draw a Number Line Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data: 4 6 840 42°14°16 18 20 22 Step 5 — Draw the Parts. main median 12 using a vertical line just above your number line: 4°68 10 12 14 16 18 20 22 * Next, draw a box using the lower and upper median lines as endpoints: | | 4 6 8 10 12 14 16 18 20 22 Step 5 — Draw the Parts, the whiskers(small amount) extend out to the data's smallest number 5 and largest number 20: | || 4 6 8 10 12 14 16 18 20 22 Step 6 - Label the Parts of a Box Lower Quartile Median _ Upper Quartile Lower Extreme Upper Extreme Hy 4 6 8 10 12 14 16 18 20 22 * Name the parts of a Box-Plot Interquartile Range The interquartile range is the difference between the upper quartile and the lower quartile. 14- 8.5 WHAT IS A CARTOGRAM * A cartogram is a colored map that gives a graphical representation of statistical data. “It is used for an immediate view of a phenomenon or behavior.