12.2 – statistical analysis. measures of central tendency

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?

Vegetable Calories Vegetable CaloriesAsparagus 14 Cauliflower 10Beans 30 Celery 17Bell pepper 20 Corn 66Broccoli 25 Lettuce 9Cabbage 17 Spinach 9Carrots 28 Zucchini 17

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

Vegetable Calories Vegetable CaloriesAsparagus 14 Cauliflower 10Beans 30 Celery 17Bell pepper 20 Corn 66Broccoli 25 Lettuce 9Cabbage 17 Spinach 9Carrots 28 Zucchini 17

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?

9,9,10,14,17,17,17,20,25,28,30,66Since 66 is much larger than the other numbers it would skew the results of the mean.

Vegetable Calories Vegetable CaloriesAsparagus 14 Cauliflower 10Beans 30 Celery 17Bell pepper 20 Corn 66Broccoli 25 Lettuce 9Cabbage 17 Spinach 9Carrots 28 Zucchini 17

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?

9,9,10,14,17,17,17,20,25,28,30,66Since 66 is much larger than the other numbers it would skew the results of the mean.Both the median and mode are 17.

Vegetable Calories Vegetable CaloriesAsparagus 14 Cauliflower 10Beans 30 Celery 17Bell pepper 20 Corn 66Broccoli 25 Lettuce 9Cabbage 17 Spinach 9Carrots 28 Zucchini 17

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

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.

• 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

= ± 0.0216

• 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

= ± 0.0216= ± 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

= ± 0.0216= ± 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

= ± 0.0216= ± 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

= ± 0.0216= ± 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 ± 0.0216

• 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

= ± 0.0216= ± 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 ± 0.0216

0.58 + 0.0216 0.58 - 0.0216

• 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

= ± 0.0216= ± 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 ± 0.02160.58 + 0.0216 0.58 - 0.0216 0.6016 0.5584

• 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

= ± 0.0216= ± 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 ± 0.02160.58 + 0.0216 0.58 - 0.0216 0.6016 0.5584 60.16% 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

= ± 0.0216= ± 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 ± 0.02160.58 + 0.0216 0.58 - 0.0216 0.6016 0.5584 60.16% 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%.