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Classroom Capsule 3 RoeAnn Barker

Measures of Central Tendency. Designed forBlitzer's Thinking MathematicallyAuthor: RoeAnn Barker. Measures of Central Tendency. MeanMedianModeMidrange. Mean. Computing the Mean. . Add the data items Divide your answer by the number of data items. Mean for a frequency distribution. Median.

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Classroom Capsule 3 RoeAnn Barker

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    1. Classroom Capsule 3 RoeAnn Barker Description: Lesson/presentation, students will develop an overview understanding of measures of central tendency Topic: central tendencies Materials: computer with means to project, whiteboard, markers, overhead transparency of normal distribution

    3. Measures of Central Tendency Mean Median Mode Midrange

    4. Mean

    5. Computing the Mean Add the data items Divide your answer by the number of data items

    6. Mean for a frequency distribution

    9. Median Arrange the data items in order, from smallest to largest If the number of data items is odd, the median is the item in the middle If the number of data items is even, the median is the mean of the two middle items

    10. Position of the Median

    11. Median for a Frequency Distribution

    12. Mode The data value that occurs most often in the data Data sets may not contain a mode Data sets may be bimodal

    13. Midrange lowest data value + highest data value 2

    14. Measures of Dispersion a measure how observations in the data set are distributed across various categories

    15. Measures of Dispersion Range Standard Deviation

    16. Range Highest date value – lowest data value

    17. Standard Deviation A measure of the variability of a distribution of data. The more the data points cluster around the mean, the smaller the standard deviation.

    18. Standard Deviation

    19. Computing Standard Deviation Step 1 Find the mean of the data 17,18,19,20,21,22,23 17 + 18 + 19 + 20 + 21 + 22 + 23 = 140 7 7 =20

    20. Computing Standard Deviation Step 2 Find deviation of each item from the mean 20 – 17 = 3 20 – 18 = 2 20 – 19 =1 20 – 20 = 0 20 – 21 = -1 20 – 22 = -2 20 – 23 = -3

    21. Computing Standard Deviation Step 3 Square each deviation

    22. Computing Standard Deviation Step 4 Sum the squared deviations 9 + 4 + 1 + 0 + 1 + 4 + 9 = 28

    23. Computing Standard Deviation Step 5 Divide Step 4 result by n – 1 (n is the number of data items)

    24. Computing Standard Deviation Step 6 Determine the square root of the result of the previous step

    26. Use Excel Tools Data Analysis Descriptive Statistics (OK) Input Range—highlight the data check summary statistics box (OK)

    28. In a normal distribution, 68% of the scores fall within one standard deviation above and one standard deviation below the mean.

    29. Normal Distribution Symmetric Mean, median mode are the same Standard deviation determines the spread of the curve Mean determines the height

    30. Normal Distribution

    31. ~68% of the data falls within one standard deviation of the mean ~95% of the data items fall within two standard deviations of the mean ~99.7% of the data items fall within three standard deviations of the mean 667

    32. IQ are normally distributed with a mean of 100 and a standard deviation of 15. What is the IQ range of 68% of people? What is the IQ range of 95% of people? What is the IQ range of 99.7% of the people?

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