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 applicants
Sample = 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 applicants
Sample = group of 40 applicants
Parameter = 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 applicants
Sample = group of 40 applicants
Parameter = all applicants’ mean GPA
Statistic = 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 area
Sample = 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 area
Sample = the nurses selected at random
Parameter = 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 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
MEASURES OF VARIATION
Type
Description
When Best Used
MEASURES OF VARIATION
Type
Range
Description
When Best Used
MEASURES OF VARIATION
Type
Range
Description
The difference
between the greatest
and least values
When Best Used
MEASURES OF VARIATION
Type
Range
Description
When Best Used
The difference
To describe which
between the greatest numbers are included
and least values
in the data set
MEASURES OF VARIATION
Type
Range
Quartile
Description
When Best Used
The difference
To describe which
between the greatest numbers are included
and least values
in the data set
MEASURES OF VARIATION
Type
Range
Quartile
Description
When Best Used
The difference
To describe which
between the greatest numbers are included
and least values
in the data set
The values that divide
the data set into four
equal parts
MEASURES OF VARIATION
Type
Range
Quartile
Description
When Best Used
The difference
between the greatest
and least values
The values that divide
the data set into four
equal parts
To describe which
numbers are included
in the data set
To determine values
in the upper or lower
portions of a data set
MEASURES OF VARIATION
Type
Range
Quartile
Interquartile range
Description
When Best Used
The difference
between the greatest
and least values
The values that divide
the data set into four
equal parts
To describe which
numbers are included
in the data set
To determine values
in the upper or lower
portions of a data set
MEASURES OF VARIATION
Type
Range
Quartile
Interquartile range
Description
When Best Used
The difference
between the greatest
and least values
The values that divide
the data set into four
equal parts
To describe which
numbers are included
in the data set
To determine values
in the upper or lower
portions of a data set
The range of the
middle half of a data
set; the difference
between the upper
and lower quartiles
MEASURES OF VARIATION
Type
Range
Quartile
Interquartile range
Description
When Best Used
The difference
between the greatest
and least values
The values that divide
the data set into four
equal parts
To describe which
numbers are included
in the data set
To determine values
in the upper or lower
portions of a data set
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 mean
Step 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 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.
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| = 18
Step 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| = 18
Step 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, 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.
• 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.
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