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12.3 – Statistics & Parameters

12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample. Statistic – a measure that describes the characteristic of a sample. Parameter – a measure that describes the characteristic of a population.

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12.3 – Statistics & Parameters

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  1. 12.3 – Statistics & Parameters

  2. Statistic – a measure that describes the characteristic of a sample.

  3. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population.

  4. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population. Ex. 1 Identify the population, sample, parameter, and statistic of each situation.

  5. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population. Ex. 1 Identify the population, sample, parameter, and statistic of each situation. • A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated.

  6. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population. Ex. 1 Identify the population, sample, parameter, and statistic of each situation. • A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated. Population = all applicants

  7. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population. Ex. 1 Identify the population, sample, parameter, and statistic of each situation. • A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated. Population = all applicants Sample = group of 40 applicants

  8. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population. Ex. 1 Identify the population, sample, parameter, and statistic of each situation. • A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated. Population = all applicants Sample = group of 40 applicants Parameter = all applicants’ mean GPA

  9. Statistic – a measure that describes the characteristic of a sample. • Parameter – a measure that describes the characteristic of a population. Ex. 1 Identify the population, sample, parameter, and statistic of each situation. • A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated. Population = all applicants Sample = group of 40 applicants Parameter = all applicants’ mean GPA Statistic = group of 40 applicants’ GPA

  10. b) A stratified random sample of registered nurses is selected from all hospitals in a three county area, and the median salary is calculated.

  11. b) A stratified random sample of registered nurses is selected from all hospitals in a three county area, and the median salary is calculated. Population = all nurses in the 3 county area

  12. b) A stratified random sample of registered nurses is selected from all hospitals in a three county area, and the median salary is calculated. Population = all nurses in the 3 county area Sample = the nurses selected at random

  13. b) A stratified random sample of registered nurses is selected from all hospitals in a three county area, and the median salary is calculated. Population = all nurses in the 3 county area Sample = the nurses selected at random Parameter = median salary of all nurses in the 3 county area

  14. b) A stratified random sample of registered nurses is selected from all hospitals in a three county area, and the median salary is calculated. Population = all nurses in the 3 county area Sample = the nurses selected at random Parameter = median salary of all nurses in the 3 county area Statistic = median salary of the nurses selected at random

  15. MEASURES OF VARIATION

  16. MEASURES OF VARIATION

  17. MEASURES OF VARIATION

  18. MEASURES OF VARIATION

  19. MEASURES OF VARIATION

  20. MEASURES OF VARIATION

  21. MEASURES OF VARIATION

  22. MEASURES OF VARIATION

  23. MEASURES OF VARIATION

  24. MEASURES OF VARIATION

  25. MEASURES OF VARIATION • Mean Absolute Variation – the average of the absolute values of the differences between the mean and each value in the data set.

  26. MEASURES OF VARIATION • Mean Absolute Variation – the average of the absolute values of the differences between the mean and each value in the data set. Step 1: Find the mean

  27. MEASURES OF VARIATION • Mean Absolute Variation – the average of the absolute values of the differences between the mean and each value in the data set. Step 1: Find the mean Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean.

  28. MEASURES OF VARIATION • Mean Absolute Variation – the average of the absolute values of the differences between the mean and each value in the data set. Step 1: Find the mean Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean. Step 3: Divide the sum by the number of values in the set of data.

  29. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth.

  30. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean.

  31. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean. (2 + 2 + 3 + 4 + 14) 5

  32. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean.(2 + 2 + 3 + 4 + 14) = 5 5

  33. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean. (2 + 2 + 3 + 4 + 14) = 5 5 Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean.

  34. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean. (2 + 2 + 3 + 4 + 14) = 5 5 Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean. |2-5|+|2-5|+|3-5|+|4-5|+|14-5|

  35. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean. (2 + 2 + 3 + 4 + 14) = 5 5 Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean. |2-5|+|2-5|+|3-5|+|4-5|+|14-5| = 18

  36. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean. (2 + 2 + 3 + 4 + 14) = 5 5 Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean. |2-5|+|2-5|+|3-5|+|4-5|+|14-5| = 18 Step 3: Divide the sum by the number of values in the set of data. 18 5

  37. Ex. 2 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. They received the following responses in one day: 2,2,3,4,14. Find the mean absolute deviation to the nearest tenth. Step 1: Find the mean. (2 + 2 + 3 + 4 + 14) = 5 5 Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean. |2-5|+|2-5|+|3-5|+|4-5|+|14-5| = 18 Step 3: Divide the sum by the number of values in the set of data. 18 = 3.6 5

  38. Standard Deviation – a calculated value that shows how the data deviates from the mean of the data, represented by σ.

  39. Standard Deviation – a calculated value that shows how the data deviates from the mean of the data, represented by σ. • Variance – the square of the standard deviation.

  40. Standard Deviation – a calculated value that shows how the data deviates from the mean of the data, represented by σ. • Variance – the square of the standard deviation. Step 1: Find the mean, x

  41. Standard Deviation – a calculated value that shows how the data deviates from the mean of the data, represented by σ. • Variance – the square of the standard deviation. Step 1: Find the mean, x Step 2: Find the square of the differences between each value in the set of data and the mean. Then add and divide by the number of values in the set of data. This is the variance.

  42. Standard Deviation – a calculated value that shows how the data deviates from the mean of the data, represented by σ. • Variance – the square of the standard deviation. Step 1: Find the mean, x Step 2: Find the square of the differences between each value in the set of data and the mean. Then add and divide by the number of values in the set of data. This is the variance. Step 3: Take the square root of the variance. This is the standard deviation.

  43. Ex. 3Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth.

  44. Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth. Step 1: Find the mean, x

  45. Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth. Step 1: Find the mean, x x = 3+6+11+12+13 5

  46. Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth. Step 1: Find the mean, x x = 3+6+11+12+13 = 9 5

  47. Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth. Step 1: Find the mean, x x = 3+6+11+12+13 = 9 5 Step 2: Find the square of the differences between each value in the set of data and the mean. Then add and divide by the number of values in the set of data. This is the variance.

  48. Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth. Step 1: Find the mean, x x = 3+6+11+12+13 = 9 5 Step 2: Find the square of the differences between each value in the set of data and the mean. Then add and divide by the number of values in the set of data. This is the variance. σ2 = (3-9)2+(6-9)2+(11-9)2+(12-9)2+(13-9)2 5

  49. Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth. Step 1: Find the mean, x x = 3+6+11+12+13 = 9 5 Step 2: Find the square of the differences between each value in the set of data and the mean. Then add and divide by the number of values in the set of data. This is the variance. σ2 = (3-9)2+(6-9)2+(11-9)2+(12-9)2+(13-9)2= 14.8 5

  50. Step 3: Take the square root of the variance. This is the standard deviation.

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