Statistics | Mathematics

LESSON

Statistics

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11th grade

Mathematics, Other

3 days ago by

10 slides

Statistics

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Types

1. Descriptive Statistics

Process raw numerical data into graphs, charts, other meaningful (mean, mode, median, tables, Standard Deviation) forms.

2. Inferential Statistics

When you make generalizations , decisions , conclusions based on the data presented.

Key Terms

1) Population - the total amount of objects under study.

2) Sample - a representative of the population

3) Data :

* Numerical ; Eg height in cm

* Non-numerical ; Eg colour

4) Classification :

*Primary data - first hand data collected

* Secondary data - data collected from other sources E.g. internet , newspapers

5) Data :

Quantitative - data recorded in numeric form E.G height, date

Qualitative - data recorded in non-numeric form E.G. colour of vehicles

Discrete - can only have exact values / There is a distinct gap between values E.G shoe sizes, cash in hand, number of siblings

Continuous - a variable is said to be continuous if it is approximated at different levels of precision E.G height, mass, area, volume

1) STEM AND LEAF PLOT

A useful way of grouping data into classics while still retaining the original data is to use a stem and leaf plot. In a stem and leaf diagram , numerical digits are used to represent the data instead of using lines and dots. The stem and leaf consist of 2 parts. The stem can have 1 or more digits but the leaf only has one digit ( the last digit). A stem and leaf plot can also be drawn back to back.

Properties :

1. Leaf units are order (ascending)

2. No commas

3. Digits must line up one below the other

4. Must include a small key.

Advantages :

1. It uses ALL the values in the diagram .

2. Can calculate Mean, Mode , Median quartiles from it.

Example 1

The following marks are obtained in a French test of 20 students.
75, 69, 58, 58, 46, 44, 32, 50, 53, 78, 81, 61, 61, 45, 31, 44, 53, 66, 47, 57.
Construct a stem and leaf diagram for the data given and determine the median mark.
Data = 20

\therefore Median\ =\frac{10th\ +\ 11th\ }{2}

=\frac{53+57}{2}

=\frac{110}{2}

=55

Ex 2

Questionnaires were given to 30 patients. Some were *posted out* and some were *given by hand*. The data below is the room number of each patient who received a questionnaire.

Posted out :

11, 19, 22, 25, 25, 29, 31, 34, 36, 38, 40, 46, 49, 50, 50.

By Hand:

15, 15, 21, 22, 23, 25, 26, 31, 33, 34, 37, 39, 41, 46, 46.

Determine the mode and median of each set of data.

Posted:

Mode = 25, 50

Median =34

By hand :

Mode = 15, 46

Median = 31