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.

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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

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. =

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. Note how the coding helped to simplify the calculations by making the numbers smaller.

Example: Find the mean and the standard deviation of the values in the table. Use the transformation below to help you. Coding x Frequency y Using the given transformation, add a y column to the table.

Coding y Frequency, f 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.

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 y mean Y = mean X = sd Y = sd X =

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.

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