2. Aims: To be able to calculate the mean and s.d. using the coding method To be able to use summarised data to find the mean and s.d. Representing data Lesson 4

3. Coding is a technique that can simplify the numerical effort required in finding a mean or standard deviation. Coding How do you think multiplying and adding effects the mean and standard deviation? Original mean = Original population s.d. = Transformed mean = Transformed s.d. = Transformed mean = Transformed s.d. =

4. Adding So, if a number b is added to each piece of data, the mean value is also i_____________ by b. The standard deviation is u_____________. Coding Multiplying If each piece of data is multiplied by a, the mean value is m________________ by a. The standard deviation is a________ multiplied by a. http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=gcseStats/sd/stdDev6Change Note how the coding helped to simplify the calculations by making the numbers smaller.

5. Example: Find the mean and the standard deviation of the values in the table. Use the transformation below to help you. Coding x Frequency 503 605 707 804 901 y 0 1 2 3 4 Using the given transformation, add a y column to the table.

6. Coding y Frequency, f 03 15 27 34 41 Total 20 To find the mean: To find the s.d.: And the standard deviation of x is: We can rearrange: to get: Therefore the mean of x is: To find them for the x values, you must reverse the coding.

7. Example: Find the mean and the standard deviation of the values in the table. Use the transformation below to help you. On w/b x Frequency 882 646 329 961 1127 y mean Y = mean X = sd Y = sd X =

8. Using coding given summarised data The heights of a full class of 80 students are summarised by the equations Find the mean and standard deviation of the 80 students. Let y = x – 160 and then Therefore the mean of the x-values is The mean of the y-values is given by: Therefore the standard deviation of the x-values is ___ as it is unchanged by adding a constant to the code.

9. On w/b The heights of a full class of 80 students are summarised by the equations Find the mean and standard deviation of the 80 students. Let y = x – 148 and then 1.Try Worksheet 2. Do Linear Coding Puzzle