The student should be able to study a statistical series by determining its mean or median knowing the value of the total number of people. Develop skills in representing a pie chart, histogram or bar graph. Master its various definitions by determining the population of a statistical series and the character studied. We will end this lesson by looking at real life examples from the ninth grade.
I. The statistical series
1. General vocabulary
When conducting a survey, one is led to study characteristics (theme of the survey) specific to each individual.
- The set of individuals is called the population.
- The character can be qualitative (hair color, sports practiced or favorite movie) or quantitative (height, age, time spent in front of the television, …).
- The total number of individuals in the population is called the total number of individuals and noted N.
- The number of individuals who have the same characteristic is called the number of individuals of the characteristic.
Statistics is a branch of mathematics that studies a character in a population.
1) Study the set of test scores (trait) in a class (population).
2) Study voting intentions for elections (character) on a sample of 1,000 people.
A statistical series is the data of a series of numbers presented in the form of a list or a table.
Example: transcript of a math test.
II The mean and range of a statistical series
The mean of a statistical series is the quotient of the sum of all the values of this series by the total number of people.
with: the number of characters and the values of the character.
N being the total number of employees with .
We have a sequence of notes: 5; 12; 19; 12; 8; 10; 11; 14; 3; 8; 7; 12; 10; 9; 8; 16; 14; 8; 5; 11.
Calculate the average of these scores:
The frequency of a value of a characteristic is the quotient of the number of the value of the characteristic by the total number of people.
The frequency f in % represents the percentage of the workforce in relation to the total workforce.
Using the previous series of notes, calculate the frequencies and then the mean of this statistical series.
Concrete meaning of the average :
If each student were to get the same score then each student would get 10.1 out of 20.
The range of a statistical series is the difference between the largest and smallest values in the series.
In the previous series, the range of notes is: 19-3 = 6.
III. The median of a statistical series
The median of an ordered statistical series is a value of the character that divides the series into two groups of equal size such that :
- a group contains values less than or equal to the median ;
- the other group contains values greater than or equal to the median.
Example : case of an odd number of values.
Here are the grades of a group of 9 students on a math assignment.
First you have to arrange the numbers in ascending order: 5< 6 <6 <8<11<12<13<13<14
The median of this statistical series is the fifth value, so 11.
Example : case of an even number of values.
Here are the grades of a group of 6 students on a physical science assignment.
First you have to arrange the numbers in ascending order: 5<6<13<14<16<18
The median of this statistical series is the average between the third and fourth values.
Concrete meaning of the median:
There are as many students who scored below 13.5 as there are students who scored above 13.5.
Skills to learn about statistics:
- Know the definition of a population and a characteristic;
- Calculate a frequency and an average;
- To know how to determine the median of a statistical series according to the parity of the total number;
- Use graphical representations such as pie charts, bar graphs and histograms.
These exercises are in accordance with the officialnational education programs.
In addition, you can consult the exercises on statistics in third grade.
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