STANDARD DEVIATION

Name: ___________________________________________ Section: ___________________________ Semester _________________ Date: ____________________ This worksheet will walk you through how to calculate the standard deviation. Activity 1: CALCULATING STANDARD DEVIATION The standard deviation is used to tell how on average any data point is far from the mean. The smaller the standard deviation, the closer the scores on average are to the mean. When the standard deviation is large, the scores are more widely spread on average from the mean The standard deviation is calculated as the average distance from the mean. Practice Problem #1: The junior high basketball team played ten games. Find the standard deviation for the number of baskets scored by the team for the ten games: 8, 4, 6, 6, 7, 7, 9, 4, 8, 5. Follow the steps below to calculate the standard deviation. Step 1: Average the scores in the Score column of the table below in the order from the smallest to the largest. Step 2: Find the mean of the data set and place your answer below on Line A. Step 3: Subtract the mean from each of the scores in the data set. Record the difference in the column titled “Difference from the Mean” column in the table below. Be sure to record whether the answer is positive or negative, i.e.: 4-5 = -1, 7-5 = 2 Step 4: Find the square of each number in the “Difference from The Mean” column and record the result in the Square of the Difference column, i.e.: (1) 2 = 1 Step 5: The number of items in the data set in labeled n. Record the number in this data set on Line B below. Step 6: Find the sum of the numbers in the “Square of the Difference” and record your answer in the table. Step 7: Take the Sum of the (Difference from the Mean) 2 and divide it by n. Record your answer on Line C below Step 8: The square root of Line C is the standard deviation. Record your answer on Line D below: Number Difference from the Mean (x̅ –X) (Difference from the Mean)2 (Square of the Difference) Sum of (Difference from the mean) 2: _________________ A. Mean (x̅) : ________________ B. (number of observations) n:_____________________ C. Sum of (Difference from the Mean) 2 D. Find the Variance (σ2) by Dividing {Sum of (Difference from the Mean) 2} by (n): Variance (σ2) ____________. E. Find the Standard deviation (s) by finding the square root of the Variance. Standard Deviation (s) = ______________. Practice Problem #2 Find the standard deviation for the following test scores. Use the chart below to record the steps: 85, 100, 92, 96, 87, 94, 75. Score Difference from the Mean (x̅ –X) (Difference from the Mean) 2 (Square of the Difference) Sum of (Difference from the Mean) 2: ________________. A. Mean (x̅) : ________________ B. (number of observations) n:_____________________ C. Sum of (Difference from the Mean) 2 D. Find the Variance (σ2) by Dividing {Sum of (Difference from the Mean) 2} by (n): Variance (σ2) ____________. E. Find the Standard deviation (s) by finding the square root of the Variance. Standard Deviation (s) = ______________. Practice Problem #3 Find the standard deviation for the following test scores. Use the chart below to record the steps: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29. Score Difference from the Mean (x̅ –X) (Difference from the Mean) 2 (Square of the Difference) Sum of (Difference from the Mean) 2: ________________. A. Mean (x̅) : ________________ B. (number of observations) n:_____________________ C. Sum of (Difference from the Mean) 2 D. Find the Variance (σ2) by Dividing {Sum of (Difference from the Mean) 2} by (n): Variance (σ2) ____________. E. Find the Standard deviation (s) by finding the square root of the Variance. Standard Deviation (s) = ______________.