12.3 – statistics & parameters. statistic – a measure that describes the characteristic of a...
TRANSCRIPT
![Page 1: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/1.jpg)
12.3 – Statistics & Parameters
![Page 2: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/2.jpg)
• Statistic – a measure that describes the characteristic of a sample.
![Page 3: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/3.jpg)
• Statistic – a measure that describes the characteristic of a sample.
• Parameter – a measure that describes the characteristic of a population.
![Page 4: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/4.jpg)
• 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.
![Page 5: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/5.jpg)
• 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.
![Page 6: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/6.jpg)
• 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
![Page 7: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/7.jpg)
• 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
![Page 8: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/8.jpg)
• 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
![Page 9: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/9.jpg)
• 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
![Page 10: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/10.jpg)
b) A stratified random sample of registered nurses is selected from all hospitals in a three county area, and the median salary is calculated.
![Page 11: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/11.jpg)
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
![Page 12: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/12.jpg)
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
![Page 13: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/13.jpg)
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
![Page 14: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/14.jpg)
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
![Page 15: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/15.jpg)
MEASURES OF VARIATIONType Description When Best Used
![Page 16: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/16.jpg)
MEASURES OF VARIATIONType Description When Best Used
Range
![Page 17: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/17.jpg)
MEASURES OF VARIATIONType Description When Best Used
Range The difference between the greatest and least values
![Page 18: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/18.jpg)
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
![Page 19: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/19.jpg)
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
![Page 20: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/20.jpg)
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
![Page 21: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/21.jpg)
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
![Page 22: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/22.jpg)
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
![Page 23: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/23.jpg)
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
![Page 24: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/24.jpg)
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
![Page 25: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/25.jpg)
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.
![Page 26: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/26.jpg)
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
![Page 27: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/27.jpg)
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.
![Page 28: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/28.jpg)
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.
![Page 29: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/29.jpg)
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.
![Page 30: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/30.jpg)
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.
![Page 31: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/31.jpg)
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
![Page 32: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/32.jpg)
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
![Page 33: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/33.jpg)
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.
![Page 34: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/34.jpg)
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|
![Page 35: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/35.jpg)
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
![Page 36: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/36.jpg)
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
![Page 37: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/37.jpg)
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
![Page 38: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/38.jpg)
• Standard Deviation – a calculated value that shows how the data deviates from the mean of the data, represented by σ.
![Page 39: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/39.jpg)
• 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.
![Page 40: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/40.jpg)
• 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
![Page 41: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/41.jpg)
• 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.
![Page 42: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/42.jpg)
• 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.
![Page 43: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/43.jpg)
Ex. 3 Find the mean, variance, and standard deviation of 3,6,11,12,13 to the nearest tenth.
![Page 44: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/44.jpg)
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
![Page 45: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/45.jpg)
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
![Page 46: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/46.jpg)
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
![Page 47: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/47.jpg)
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.
![Page 48: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/48.jpg)
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
![Page 49: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/49.jpg)
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
![Page 50: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/50.jpg)
Step 3: Take the square root of the variance. This is the standard deviation.
![Page 51: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/51.jpg)
Step 3: Take the square root of the variance. This is the standard deviation.
σ2 = 14.8
![Page 52: 12.3 – Statistics & Parameters. Statistic – a measure that describes the characteristic of a sample](https://reader035.vdocuments.site/reader035/viewer/2022062717/56649e445503460f94b38699/html5/thumbnails/52.jpg)
Step 3: Take the square root of the variance. This is the standard deviation.
σ2 = 14.8 σ ≈ 3.8