12.2 – Statistical Analysis

Measures of Central Tendency

Measures of Central Tendency Mean – the sum of the data divided by the number of items in the data set.

Measures of Central Tendency Mean – the sum of the data divided by the number of items in the data set. Median – the middle number of the ordered data or the mean of the middle two numbers.

Measures of Central Tendency Mean – the sum of the data divided by the number of items in the data set. Median – the middle number of the ordered data or the mean of the middle two numbers. Mode – the number or numbers that occur most often.

Ex. 1 The table shows the number of Calories per serving of each vegetable. Which measure of central tendency best represents the data, if any? VegetableCaloriesVegetableCalories Asparagus14Cauliflower10 Beans30Celery17 Bell pepper20Corn66 Broccoli25Lettuce9 Cabbage17Spinach9 Carrots28Zucchini17

Ex. 1 The table shows the number of Calories per serving of each vegetable. Which measure of central tendency best represents the data, if any? 9,9,10,14,17,17,17,20,25,28,30,66 VegetableCaloriesVegetableCalories Asparagus14Cauliflower10 Beans30Celery17 Bell pepper20Corn66 Broccoli25Lettuce9 Cabbage17Spinach9 Carrots28Zucchini17

Ex. 1 The table shows the number of Calories per serving of each vegetable. Which measure of central tendency best represents the data, if any? 9,9,10,14,17,17,17,20,25,28,30,66 Since 66 is much larger than the other numbers it would skew the results of the mean. VegetableCaloriesVegetableCalories Asparagus14Cauliflower10 Beans30Celery17 Bell pepper20Corn66 Broccoli25Lettuce9 Cabbage17Spinach9 Carrots28Zucchini17

Ex. 1 The table shows the number of Calories per serving of each vegetable. Which measure of central tendency best represents the data, if any? 9,9,10,14,17,17,17,20,25,28,30,66 Since 66 is much larger than the other numbers it would skew the results of the mean. Both the median and mode are 17. VegetableCaloriesVegetableCalories Asparagus14Cauliflower10 Beans30Celery17 Bell pepper20Corn66 Broccoli25Lettuce9 Cabbage17Spinach9 Carrots28Zucchini17

Parameter – a measure that represents a characteristic of a population.

Statistic – a measure that represents a characteristic of a sample.

Parameter – a measure that represents a characteristic of a population. Statistic – a measure that represents a characteristic of a sample. Ex. 2 Determine whether each of the following represents a population or a sample.

Parameter – a measure that represents a characteristic of a population. Statistic – a measure that represents a characteristic of a sample. Ex. 2 Determine whether each of the following represents a population or a sample. a)The Nielsen Poll estimates the average number of hours of T.V. watched per week for U.S. households.

Parameter – a measure that represents a characteristic of a population. Statistic – a measure that represents a characteristic of a sample. Ex. 2 Determine whether each of the following represents a population or a sample. a)The Nielsen Poll estimates the average number of hours of T.V. watched per week for U.S. households. Sample b/c not all U.S. citizens were polled.

Parameter – a measure that represents a characteristic of a population. Statistic – a measure that represents a characteristic of a sample. Ex. 2 Determine whether each of the following represents a population or a sample. a)The Nielsen Poll estimates the average number of hours of T.V. watched per week for U.S. households. Sample b/c not all U.S. citizens were polled. b)A math exam is given to every graduating senior in the country to analyze certain math skills.

Parameter – a measure that represents a characteristic of a population. Statistic – a measure that represents a characteristic of a sample. Ex. 2 Determine whether each of the following represents a population or a sample. a)The Nielsen Poll estimates the average number of hours of T.V. watched per week for U.S. households. Sample b/c not all U.S. citizens were polled. b)A math exam is given to every graduating senior in the country to analyze certain math skills. Population b/c all seniors in the U.S. took the exam.

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population.

= ± 1_ √n

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport.

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error?

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ±

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16%

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport?

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport? 58% ± 2.16%

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport? 58% ± 2.16% 0.58 ±

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport? 58% ± 2.16% 0.58 ±

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport? 58% ± 2.16% 0.58 ±

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport? 58% ± 2.16% 0.58 ± % 55.84%

Margin of Sampling Error – an interval that shows how much of the responses from the sample would differ from the population. = ± 1_ √n Ex. 3 In a random survey of 2148 people, 58% said that football is their favorite sport. a)What is the margin of sampling error? = ± 1_ √n = ± 1_ √2148 = ± = ± 2.16% b)What is the likely interval that contains the percentages of the population that claims football is their favorite sport? 58% ± 2.16% 0.58 ± % 55.84% The likely interval that contains the percentage of the population that claims football is their favorite sport is between 55.84% and 60.16%.