Two-Way Tables & Stepped Tables Mathematics Two-Way Tables & Stepped Tables

Lesson Objectives The aim of this powerpoint is to help you… to learn how to complete, read and interpret a two-way table to learn how to use a stepped table

Two-Way Tables This table is used to summarise data using two different criteria. One criterion will apply to the rows of the table and the other criterion will apply to the columns. The total number of objects included in the data will EITHER equate to the total of the rows OR the total of the columns (they should be equal!).

Two-Way Tables Read the question carefully and find the correct row(s) and/or column(s) referred to, in order to work out the answer. If there are missing values in the table, use the information you have been given in the question to work out the missing values. Remember, rows should have a total at the end – subtract individual row values from the row total to find missing row values. Remember columns should have a total at the bottom – subtract individual column values from the column total to find missing column values.

Using Two-Way Tables - Example The two way table below shows the genders and writing hands of students in a small primary school. You will need to use this table to answer the questions that follow. GIRLS BOYS RIGHT-Handed 52 83 LEFT-Handed 6 8

Using Two-Way Tables - Example Q1. How many girls write with their left hand? HINT: Look down the ‘girls’ column and across the ‘left’ row. What value is in the overlapping section? ANS. 6 GIRLS BOYS RIGHT-Handed 52 83 LEFT-Handed 6 8

Using Two-Way Tables - Example Q2. How many girls are there altogether? HINT: Look down the ‘girls’ column and total these values. ANS. 52 + 6 = 58 GIRLS BOYS RIGHT-Handed 52 83 LEFT-Handed 6 8

Using Two-Way Tables - Example Q3. How many students are right-handed? HINT: Look across the ‘right-handed’ row and total these values. ANS. 52 + 83 = 135 GIRLS BOYS RIGHT-Handed 52 83 LEFT-Handed 6 8

Using Two-Way Tables - Example Q4. How many students are there altogether? HINT: Add ALL the values together. ANS. 52 + 83 + 6 + 8 = 149 GIRLS BOYS RIGHT-Handed 52 83 LEFT-Handed 6 8

Completing Two-Way Tables - Example This table shows the genders and dominant hands of another group of students. There are 50 students in the class and 7 are left-handed. Fill-in the missing table values. Let’s do this step-by-step… GIRLS BOYS LEFT-Handed 2 RIGHT-Handed 17

Completing Two-Way Tables - Example First let’s put in the total rows and columns… Now let’s put in the fact we have been told that are 50 students in the class… Finally we are also told 7 students are left-handed… GIRLS BOYS LEFT-Handed 2 RIGHT-Handed 17 GIRLS BOYS TOTAL LEFT-Handed 2 RIGHT-handed 17 7 50

Completing Two-Way Tables - Example Left-handed row: 2 + ? = 7 …. Boys = 7 – 2 = 5 Total column: 7 + ? = 50 … Right = 50 – 7 = 43 Boys column: 5 + 17 = 22 GIRLS BOYS TOTAL LEFT-Handed 2 7 RIGHT-handed 17 50 5 43 22

Completing Two-Way Tables - Example Right-handed row: ? + 17 = 43 …. Girls = 43 – 17 = 26 Girls column: 2 + 26 = 28 CHECK using Total row: 28 + 22 = 50 (Yes) GIRLS BOYS TOTAL LEFT-Handed 2 5 7 RIGHT-handed 17 43 22 50 26 28

Stepped Tables This type of table again has two directions (rows and columns) but usually applies to one criterion. These tables are usually used to indicate distances between places. Place names appear in both a row and a column – there are two ways of displaying them too! Distances between places are where those places’ rows and/or columns overlap.

Stepped Tables - Example Both stepped tables below show the distances between 5 towns (A to E). They are merely labelled slightly differently. The one on the right is the more typical style of labelling. A B C D E 7 12 23 35 5 19 40 13 58 62 7 12 23 35 5 19 40 13 58 62 B C D E A B C D

Stepped Tables - Example How far is it from B to C? HINT: Which row/column do B and C overlap in? ANS. 5 A B C D E 7 12 23 35 5 19 40 13 58 62 7 12 23 35 5 19 40 13 58 62 B C D E A B C D

What next? Print out and read through the notes called Data8a & Data8b. Work through the MyMaths lesson and then its online homework called Two Way Tables which can be found at: Lesson: http://app.mymaths.co.uk/356-resource/two-way-tables Online HW: http://app.mymaths.co.uk/356-homework/two-way-tables Answer the tasks that appear in the Data8a & Data8b notes. Learn about another type of stepped representation by working through the MyMaths lesson and then its online homework called Step Graphs found at: Lesson: http://app.mymaths.co.uk/360-resource/step-graphs Online HW: http://app.mymaths.co.uk/360-homework/step-graphs Now move on to the Data-9 powerpoint