1. By: Ms. Amani Albraikan

2.  The frequency of a particular data value is the number of times the data value occurs.  For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f.  A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.

3.  Example 5  The marks awarded for an assignment set for a Year 8 class of 20 students were as follows: 6 7 5 7 7 8 7 6 9 7 4 10 6 8 8 9 5 6 4 8  Present this information in a frequency table.  Solution:  To construct a frequency table, we proceed as follows:

4.  In general:  We use the following steps to construct a frequency table:  Step 1:  Construct a table with three columns. Then in the first column, write down all of the data values in ascending order of magnitude.  Step 2:  To complete the second column, go through the list of data values and place one tally mark at the appropriate place in the second column for every data value. When the fifth tally is reached for a mark, draw a horizontal line through the first four tally marks as shown for 7 in the above frequency table. We continue this process until all data values in the list are tallied.  Step 3:  Count the number of tally marks for each data value and write it in the third column.

5.  Step 1:  Construct a table with three columns. The first column shows what is being arranged in ascending order (i.e. the marks). The lowest mark is 4. So, start from 4 in the first column as shown below.

7.  Step 2:  Go through the list of marks. The first mark in the list is 6, so put a tally mark against 6 in the second column. The second mark in the list is 7, so put a tally mark against 7 in the second column. The third mark in the list is 5, so put a tally mark against 5 in the third column as shown below.

8. We continue this process until all marks in the list are tallied.

9.  Step 3:  Count the number of tally marks for each mark and write it in third column. The finished frequency table is as follows:

11.  When the set of data values are spread out, it is difficult to set up a frequency table for every data value as there will be too many rows in the table. So we group the data into class intervals (or groups) to help us organise, interpret and analyse the data.frequency table  Ideally, we should have between five and ten rows in a frequency table. Bear this in mind when deciding the size of the class interval (or group).  Each group starts at a data value that is a multiple of that group. For example, if the size of the group is 5, then the groups should start at 5, 10, 15, 20 etc. Likewise, if the size of the group is 10, then the groups should start at 10, 20, 30, 40 etc.  The frequency of a group (or class interval) is the number of data values that fall in the range specified by that group (or class interval).

12.  Example 6  The number of calls from motorists per day for roadside service was recorded for the month of December 2003. The results were as follows:  Set up a frequency table for this set of data values.

13.  Solution:  To construct a frequency table, we proceed as follows:

14.  Step 1: Construct a table with three columns, and then write the data groups or class intervals in the first column. The size of each group is 40. So, the groups will start at 0, 40, 80, 120, 160 and 200 to include all of the data. Note that in fact we need 6 groups (1 more than we first thought).

16.  Step 2: Go through the list of data values. For the first data value in the list, 28, place a tally mark against the group 0-39 in the second column. For the second data value in the list, 122, place a tally mark against the group 120-159 in the second column. For the third data value in the list, 217, place a tally mark against the group 200-239 in the second column.

17. We continue this process until all of the data values in the set are tallied.

18.  Step 3: Count the number of tally marks for each group and write it in the third column. The finished frequency table is as follows:

20.  Statistical graphs are often used to display the data values of a random sample. In the following sections, we will consider bar charts, pie charts and line graphs.samplebar chartspie chartsline graphs

21.  Bar charts are often used to present data in a pictorial form to illustrate the information collected and highlight important points. They are especially useful to depict monthly car production, monthly sales, quarterly profit, average annual rainfall etc. A bar chart provides a useful comparison of data over time. The height of each bar shows the total amount of the item of interest for each month (or year).  Bar charts are drawn with parallel bars placed vertically (or horizontally). The width of each bar and the spacing between the bars are kept the same to avoid giving a misleading representation. The height of the bar is drawn to scale to represent the amount of the item.

22.  Example 8  The yearly production of cars by a particular company is recorded as follows:  Draw a bar chart to display this information.  Solution:

24.  Note the following:  It is simple to read a bar chart. Just look at the required bar and read off the value. E.g. The bar chart shows that the number of cars produced was 160 000 in 2001, 200 000 in 2002 and 320 000 in 2003.

25.  Pie charts are useful to compare different parts of a whole amount. They are often used to present financial information. E.g. A company's expenditure can be shown to be the sum of its parts including different expense categories such as salaries, borrowing interest, taxation and general running costs (i.e. rent, electricity, heating etc).sum  A pie chart is a circular chart in which the circle is divided into sectors. Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set.circlesectorspercentagefraction

26.  Example 9  A family's weekly expenditure on its house mortgage, food and fuel is as follows:  Draw a pie chart to display the information.

27.  Solution:  We can find what percentage of the total expenditure each item equals.  Percentage of weekly expenditure on:  To draw a pie chart, divide the circle into 100 percentage parts. Then allocate the number of percentage parts required for each item.

29.  Note:  It is simple to read a pie chart. Just look at the required sector representing an item (or category) and read off the value. For example, the weekly expenditure of the family on food is 37.5% of the total expenditure measured.  A pie chart is used to compare the different parts that make up a whole amount

30.  A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends. That is, finding a general pattern in data sets including temperature, sales, employment, company profit or cost over a period of time.

31. Example 10 A cylinder of liquid was heated. Its temperature was recorded at ten- minute intervals as shown in the following table.

32.  a. Draw a line graph to represent this information. b. Estimate the temperature of the cylinder after 25 minutes of heating.  Solution:  b. The estimated temperature after 25 minutes of heating is 52°C.

33.  To choose an appropriate statistical graph, consider the set of data values. In general, use the following guidelines:  Use a bar chart if you are not looking for trends (or patterns) over time; and the items (or categories) are not parts of a whole.bar chart  Use a pie chart if you need to compare different parts of a whole, there is no time involved and there are not too many items (or categories).pie chart  Use a line graph if you need to see how a quantity has changed over time. Line graphs enable us to find trends (or patterns) over time.line graph 