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.

• 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.

• 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) A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated.

• 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) 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

• 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) A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated.

Population = all applicantsSample = group of 40 applicants

• 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) A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated.

Population = all applicantsSample = group of 40 applicantsParameter = all applicants’ mean GPA

• 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) A random sample of 40 scholarship applicants at a university is selected. The mean grade-point average of the applicants is calculated.

Population = all applicantsSample = group of 40 applicantsParameter = all applicants’ mean GPAStatistic = group of 40 applicants’ GPA

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

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

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 areaSample = the nurses selected at random

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 areaSample = the nurses selected at randomParameter = median salary of all nurses in

the 3 county area

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 areaSample = the nurses selected at randomParameter = median salary of all nurses in

the 3 county areaStatistic = median salary of the nurses

selected at random

MEASURES OF VARIATIONType Description When Best Used

MEASURES OF VARIATIONType Description When Best Used

Range

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

Quartile

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

Quartile The values that divide the data set into four equal parts

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

Quartile The values that divide the data set into four equal parts

To determine values in the upper or lower portions of a data set

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

Quartile The values that divide the data set into four equal parts

To determine values in the upper or lower portions of a data set

Interquartile range

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

Quartile The values that divide the data set into four equal parts

To determine values in the upper or lower portions of a data set

Interquartile range The range of the middle half of a data set; the difference between the upper and lower quartiles

MEASURES OF VARIATIONType Description When Best Used

Range The difference between the greatest and least values

To describe which numbers are included in the data set

Quartile The values that divide the data set into four equal parts

To determine values in the upper or lower portions of a data set

Interquartile range The range of the middle half of a data set; the difference between the upper and lower quartiles

To determine what values lie in the middle half of the data set

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.

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

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 meanStep 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean.

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 meanStep 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.

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.

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.

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

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

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.

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|

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

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| = 18Step 3: Divide the sum by the number of values in the set of data. 18

5

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| = 18Step 3: Divide the sum by the number of values in the set of data. 18 = 3.6

5

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

• 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.

• 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

• 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, xStep 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.

• 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, xStep 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.

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

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

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

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

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.

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

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

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

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

σ2 = 14.8

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

σ2 = 14.8 σ ≈ 3.8