LESSON
Statistics
3 days ago by
10 slides

Statistics

Body text

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.

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

Ex 3

The heights of 20 plants are listed below.
178, 189, 147, 147, 166, 153, 171, 164, 158, 189, 166, 165, 155, 152, 147, 158, 148, 151, 172.
Determine (a) the mode, (b) median and (c) range heights.

(a) mode = 147
(b)  $Median\ =\ \frac{10th\ +11th\ }{2}$

$=\frac{158+164}{2}$
$=161$
(c)  $Range\ =\ highest\ height\ -lowest\ height$
$189\ -147=42$

2018 7 a (i)

The number of runs scored by a cricketer for 18 consecutive innings is illustrated in the following stem - and - leaf diagram.
(i) Determine the median score.

$Median\ =\frac{9th\ +\ 10th\ }{2}$
$=\frac{19+24}{2}$
$=21.5$

2019 7 a(i)

The weights, in kilograms, of students in a grade 5 class are displayed in the following stem and leaf diagram.

(i) State the number of students in the class.

(i) 29 students