Measures of Central Tendency: Mean: Mean is the most common measure of central tendency. It is...

 

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Measures of Central Tendency: Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average. Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers. Mode: Mode is the value that occurs most frequently in a set of data. Measures of Spread: (Range, Variance, Standard Deviation): Range: Difference between highest and lowest score (data value) The standard deviation is used to tell how far on average any data point is from the mean. The smaller the standard deviation, the closer the scores are on average to the mean. When the standard deviation is large, the scores are more widely spread out on average from the mean. (Variance is before taking the square root-see below) The standard deviation is calculated to find the average distance from the mean. Practice Problem #1: Calculate the standard deviation of the following test data by hand. Use the chart below to record the steps. Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 5, 100, 81, 62, 29 Test Score (x) 22 99 102 33 75 62 29 Difference from the mean (x-x) -44 33 36 -33 -9 9 34 15 -4 -37 Sum of (Difference from the mean) Σ(x-x) (Difference from the mean)² = 1019 Sum of (Difference from the Mean) divided by n -1 (sample) or n) (population):_ Σ(x - x)² (n-1) → This is called variance. Measures of Central Tendency: Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average. Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers. Mode: Mode is the value that occurs most frequently in a set of data. Measures of Spread: (Range, Variance, Standard Deviation): Range: Difference between highest and lowest score (data value) The standard deviation is used to tell how far on average any data point is from the mean. The smaller the standard deviation, the closer the scores are on average to the mean. When the standard deviation is large, the scores are more widely spread out on average from the mean. (Variance is before taking the square root-see below) The standard deviation is calculated to find the average distance from the mean. Practice Problem #1: Calculate the standard deviation of the following test data by hand. Use the chart below to record the steps. Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 5, 100, 81, 62, 29 Test Score (x) 22 99 102 33 75 62 29 Difference from the mean (x-x) -44 33 36 -33 -9 9 34 15 -4 -37 Sum of (Difference from the mean) Σ(x-x) (Difference from the mean)² = 1019 Sum of (Difference from the Mean) divided by n -1 (sample) or n) (population):_ Σ(x - x)² (n-1) → This is called variance.

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Test score Difference from the mean the mean Difference from xx x 22 ... View the full answer