Statistics Graphing Statistics & Data What is Data?. Data is organized information. It can be numbers, words, measurements, observations or even just descriptions of things. Qualitative vs Quantitative. Data can be qualitative or quantitative. Qualitative data is descriptive information (describes something) Quantitative data, is numerical information (numbers). The Quantitative data can also be Discrete or Continuous. Discrete data can only take certain values (like whole numbers) Continuous data can take any value (within a range) Example: What do we know about Arrow the Dog? Qualitative: He is brown and black He has long hair He has lots of energy Quantitative: Discrete: He has 4 legs He has 2 brothers Continuous: He weighs 25.5 kg He is 565 mm tal To help you remember think "Quantitative is about Quantity"
Collecting: Data can be collected in many ways. The simplest way is direct observation. Example: you might want to find out how many cars pass by a certain point on a road in a 10- minute interval. So: simply stand at that point on the road, and count the cars that pass by in that interval. Census or Survey A Census is when you collect data for every member of the group. A Survey is when you collect data just for selected members of the group. Example: there are 120 people in your local football club. You can ask everyone (all 120) what their age is. That is a census. Or you could just choose the people that are there this afternoon. That is a survey. A census is accurate, but hard to do. A survey is not as accurate, but may be good enough, and is a lot easier to do. Language Data or Datum?. Strictly speaking, the word data is in the plural (the singular form is datum ). However, the word is often used as if it is a singular noun. So we commonly say "the data is available" rather than the more correct way "the data are available". Frequency Distribution: Frequency is how often something occurs. Example: Sam played football on Saturday Morning, Saturday Afternoon Thursday Afternoon The frequency was 2 on Saturday, 1 on Thursday and 3 for the whole week. Frequency Distribution: values and their frequency (how often each value occurs). By counting frequencies we can make a Frequency Distribution table. Example: Goals Sam's team has scored the following numbers of goals in recent games: 2, 3, 1, 2, 1, 3, 2, 3, 4, 5, 4, 2, 2, 3
Sam put the numbers in order then added up: how often 1 occurs (2 times), how often 2 occurs (5 times), etc, and wrote them down as a Frequency Distribution table: From the table we can see interesting things such as getting 2 goals happens most frequently only once did they get 5 goals Example: Newspapers These are the numbers of newspapers sold at a local shop over the last 10 days: 22, 20, 18, 23, 20, 25, 22, 20, 18, 20 Let us count how many of each number there is: Papers Sold Frequency 18 2 19 0 20 4 21 0 22 2 23 1 24 0 25 1 It is also possible to group the values. Here they are grouped in 5s: Papers Sold Frequency 15-19 2 20-24 7 25-29 1
Presentation of Data. Data collected from various experiments does not lead to any information by itself. Hence it should be complied, classified and presented in a purposive manner to bring out important points clearly and strikingly, therefore, the manner in which statistical data is presented is of utmost importance. Charts and Diagrams Based on the data type, representation of data also differs. There are two different data types in statistics; they are: (i) discrete, and (ii) continuous type of data. i) Discrete data are distinct and separate and also invariably whole numbers, e.g. no of deaths due to particular disease. ii) Continuous data are those, which takes the value bettewn range of values, e.g. height, weight, age etc. Presenting data in charts and diagrams is useful in simplifying the presentation and enhancing comprehension of the data. Representation of data in these forms provides the following: They simplify the complexity. They facilitate visual comparison of data. They arouse the interest in reader. They save time and labour. They draw some conclusion directly or indirectly. Charts and diagrammes for discrete data 1. Bar chars: These are merely a way of presenting a set of numbers by the length of a bar; the length of the bar is proportional to the magnitude to be represented. Bar charts are easy to prepare, easy to understand and enables visual comparison. There are three types of bar chart; they are: (i) simple bar chart, (ii) multiple bar chart, and (iii) compound (or compenent or stacked) bar chart. Simple bar chart Multiple bar chart Component bar chart 2. Pie chart: Here instead of comparing the length of a bar, the areas of segments of a circle are compared. The area of each segment depends upon the percentage, which is converted to angle and drawn.
3. Pictogram: These diagrammes are used for a laymen those who cannot understand technical charts like bar charts. Here pictures or symbols are used to present the data. Charts and diagrammes for continuous data 1. Histogram: Histogram is a set of vertical bars whose areas are proportional to the frequencies represented. The class intervals are given along the horizontal axis and the frequencies along the vertical axis. 2. Line chart: It shows trends or changes in data varying with a constant, at even intervals. Although similar to an area chart, a line chart emphasises the flow of a constant and rate of change, rather than the amount of change. When you need to show trends or changes in a data at uneven or clustered intervals, an XY (scatter) chart is usually more appropriate than a line chart. 3. Frequency curve: A frequency polygon is a graphical display of a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval. The points are connected so that together with the X-axis they form a polygon.
Bar chart: A bar chart displays the frequency of data using a serie of rectangles (bars). The information on a bar chart can be obtained from a frequency table, which displays both axes of the bar chart. It is one of the most common types of charts. In a basic bar chart, ther is one bar for each value of the variable being illustrated. The length (or height) of the bar indicates the count, called the frequency of each value of the variable. They are used in order to show numbers, proportions or other ratios. The variable which is described is qualitative or discrete. The pupils in Mr. Smit's class take a Maths test and get scores out of 10, which are listed below: 2 4 5 6 2 8 1 7 8 10 6 5 7 0 2 3 9 10 1 6 They are asked to produce a vertical bar chart. Step 1. Produce a frequency table. This is a table showing the number of times each score appears. For example, the score "6" appears 3 times, so the frequency of "6" is 3. Score Frequency 0 1 1 2 2 3 3 1 4 1 5 2 6 3 7 2 8 2 9 1 10 2 Step 2. Draw the vertical bar chart. In a vertical bar chart, the frequency always goes on the vertical axis. The scores will be on the horizontal axis and there will be one vertical bar for each score. The height of each score's vertical bar is given by the frequency of that score. Don't forget to label both axis and give the graph a tittle.
Orientation of the bar chart Bar charts can be either vertical, with the bars running up and down, or horizontal, with the bars running side to side. Vertical bar chart Horizontal bar chart There are at least two types of bar chart which can be used: a multiple bar chart and a compound (or component or stacked) bar chart. Let's see them. Multiple bar charts A multiple bar chart is a different way of showing the relationship between two variables. This chart consists of groups of two or more adjacent bars separated from the next group by a gap having, ideally, a different width to the bars themselves. The diagram may be horizontal or vertical with the values either specified on the diagram or indicated using a standard axis. The following are percentage distributions of household income in two regions: Income ($'000) Region A Region B 0-10 20 10 10-20 30 20 20-30 35 30 30-40 10 20 40 or more 5 20 Total 100 100 Display the data by a multiple bar chart. Compound (or component or stacked) bar chart. In a compound bar chart the length of the complete bar signifies 100% of the population. The bar is subdivided into sections that show the relative sizes of components of population. By comparing the sizes of the subdivisions of two parallel compound bars, differences can be seen between the compositions of separate populations.
The following information shows the favourite subjects of students at a college: Favourite subject Girls Boys Mathematics 10 15 Science 5 10 Languages 15 5 Arts 20 10 Illustrate this information as a compound bar chart Histogram: is a graph that displays the classes on the horizontal axis and the frequencies of the classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is equal to the frequency of the class (when all the class widths are equal). The exam scores of a group of students are given by the following table: Score 0-19 20-39 40-59 60-79 80-99 Frequency 5 4 6 2 1 Construct the histogram. A histogram is similar to a bar graph. However bar charts are not appropiate for data with grouped frequencies for ranges of values, instead we use a histogram which is a diagram in which rectangles are used to represent frequencies. A histogram differs from the bar chart in that the rectangles may have different widths, but the key feature is that, for each rectangle area is proportional to class frequency.
Pie chart: is a graphical tool to study a population when it is divided into different categories. Each category is represented by a slice of the pie with angle at the center of the pie proportional to the frequency of the corresponding category. Patrick is carrying out a survey about where pupils do their homework. Place Home School library A friend's house No. Pupils 30 20 10 Calculate the percentages for each category and draw a pie chart. Place Home School library A friend's house No. Pupils 30 20 10 Percentage