Calculating Standard Deviation with ungrouped data
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Variance and Standard Lecture 10 Deviation (Tables) Variance and Standard Deviation Theory In this lesson: 1. Calculating standard deviation with ungrouped data. 2. Calculating standard deviation with grouped data. What you should be able to do: 1. Calculate standard deviation of tables with group or ungrouped data. Calculating Standard Deviation with ungrouped data When calculating standard deviation with frequency tables, always use the following formula: Ungrouped data π= Σππ₯π2 Σππ₯π − π π The big differences between calculating with ungrouped data and lists is that you must multiply by the frequency. 2 Step 1: Add the columns: fx, fx2, and the row: total. DO NOT ROUND YOUR DECIMALS UNTIL THE VERY END!!! STAY ORGANIZED!!!! Calculating Standard Deviation with ungrouped data When calculating standard deviation with frequency tables, always use the following formula: Ungrouped data π= Σππ₯π2 Σππ₯π − π π 2 Step 1: Add the columns: fx, fx2, and the row: total. Step 2: Fill out the new table. Step 3: Put the numbers from the “total” row into the correct parts of the formula Step 4: Subtract the two numbers Step 5: Take the square root of the variance to find the standard deviation π πΊπππ πΊππππ The big differences between calculating with ungrouped data and lists is that you must multiply by the frequency. DO NOT ROUND YOUR DECIMALS UNTIL THE VERY END!!! STAY ORGANIZED!!!! Calculating Standard Deviation with ungrouped data When calculating standard deviation with frequency tables, always use the following formula: Ungrouped data π= Σππ₯π2 Σππ₯π − π π πππ, πππ π, πππ ππ = − πππ πππ π ππ ≈ π. πππ ππππ ππππ π= πππ, πππ π, πππ − πππ πππ π ≈ π. ππ ππππ ππππ π πΊπππ πΊππππ The big differences between calculating with ungrouped data and lists is that you must multiply by the frequency. π 2 Step 1: Add the columns: fx, fx2, and the row: total. Step 2: Fill out the new table. Step 3: Put the numbers from the “total” row into the correct parts of the formula Step 4: Subtract the two numbers Step 5: Take the square root of the variance to find the standard deviation DO NOT ROUND YOUR DECIMALS UNTIL THE VERY END!!! STAY ORGANIZED!!!! Calculating Standard Deviation with ungrouped data When calculating standard deviation with frequency tables, always use the following formula: Grouped data Σππ₯ 2 Σππ₯π π= π π − π 2 Step 1: Add the columns: midpoint x, fx, fx2, and the row: total. DO NOT ROUND YOUR DECIMALS UNTIL THE VERY END!!! The big differences between calculating with grouped data and ungrouped data is that you must find the midpoint of each row. STAY ORGANIZED!!!! Calculating Standard Deviation with ungrouped data When calculating standard deviation with frequency tables, always use the following formula: Grouped data Σππ₯ 2 Σππ₯π π= π π − π 2 Step 1: Add the columns: midpoint x, fx, fx2, and the row: total. Step 2: Fill out the new table. Step 3: Put the numbers from the “total” row into the correct parts of the formula Step 4: Subtract the two numbers Step 5: Take the square root of the variance to find the standard deviation π π πΊπππ πΊππππ The big differences between calculating with grouped data and ungrouped data is that you must find the midpoint of each row. DO NOT ROUND YOUR DECIMALS UNTIL THE VERY END!!! STAY ORGANIZED!!!! Calculating Standard Deviation with ungrouped data When calculating standard deviation with frequency tables, always use the following formula: Grouped data Σππ₯ 2 Σππ₯π π= π π − π, πππ. π πππ ππ = − ππ ππ π π ππ ≈ πππ. πππ πππ π= π, πππ. π πππ − ππ ππ π ≈ ππ. ππ πππ π π πΊπππ πΊππππ The big differences between calculating with grouped data and ungrouped data is that you must find the midpoint of each row. π 2 Step 1: Add the columns: midpoint x, fx, fx2, and the row: total. Step 2: Fill out the new table. Step 3: Put the numbers from the “total” row into the correct parts of the formula Step 4: Subtract the two numbers Step 5: Take the square root of the variance to find the standard deviation DO NOT ROUND YOUR DECIMALS UNTIL THE VERY END!!! STAY ORGANIZED!!!!
