Statistical Representation (part 2)

Pie chart?

Line Graph?

Histogram?

- It’s similar to bar chart, Histogram display the graphical of data using bar with different height.

References:

Sir Habir, (2016), Lecturer of Cosmopolitan College in Commerce & Technology.

Statistical Representation (Part 1)

Types of Statistical Representation

1.  Pictograph

2. Bar charts, line graph, pie charts, Histograms and tables.

Pictograph?

- Its show the value of data by use pictures or symbols.

Example:

Number of red colored boxes sold by William, a shopkeeper, in six days of a week. See the pictograph to answer the questions.

      1)   Number of red boxes sold

Monday = 4

Tuesday = 2

Wednesday = 3

Thursday = 5

Friday = 8

Saturday = 1

Answer = 4 + 2 + 3 + 5 + 8 + 1

The sale during the week = 23

2)    The highest sale

            = on Friday which is 8

     3)  The lowest sale

           = on Saturday which is 1

Note: the answer is by observing the image above. 

Bar Charts?

It’s a vertical or horizontal bar that have two axis which is numerical value to represent the values of the data.

Example: (Vertical Bar chats) 

References:

Ghosh.P (2016).Pictograps.http://www.math-only-math.com/examples-of-pictographs.html

Web finance, (2016). Barcharts definition.http://www.businessdictionary.com/definition/bar-chart.html

Logarithm

Law of Logarithm

How to write Logarithm?

Example 1

Write the following Indices into Logarithm form.

References:

Miss Nadhirah.(2016). Lecturer of Cosmopolitan College Commerce & Technology.

Indices

Law of Indices 

Example 1

Calculate the following Indices:-

Reference:

Miss Nadhirah. (2016), Lecturer of Cosmopolitan College Commerce & Technology.

Statistical Data

What is statistical data?
- organization an collection of Numerical Data.

Types of Statistical Data?
1. Primary and Secondary data.
2. Qualitative and quantitative data.
3. Discrete and continuous.

Primary & Secondary data
- Primary data is data that collected from the sources or the investigator self.  
Example: The doctor give information to the nurse about the disease of patient.

- Secondary data is data that someone else has collected.
Example: The nurse tell the patient about he/her disease which the information of the patient disease is from the doctor.

Qualitative and Quantitative data.

- Qualitative data is data that deals with objects and characteristics and also descriptors which can be observing by someone but can’t be easily measured. Such as color, Texture or smells.

Example: 

the images show 6 speaker with different color which is purple, black, red, blue, white and green.

- Quantitative data is data that can be measured, such a height, length and width, it can be prices, area and volume and Temperature and humidity. There’s two types of Quantitative data; continuous and discrete

Continuous?

- data can be measured.

  example: The height of building

Discrete?

- data can be counted.

 example:  we can count the apples

Two apples

References:

Keith,G (2005). Quantitative. https://www.andrews.edu/~calkins/math/edrm611/edrm01.htm#QUANTITATIVE
wikibooks. (2016). Different types of Quantitative and Qualitative.https://en.wikibooks.org/wiki/Statistics/Different_Types_of_Data/Quantitative_and_Qualitative_Data

Permutation & Combination

Permutation?

Number of different ways that a certain number of objects can be ARRANGED in order from a large of objects

•          Order matter, an ordered list.
•         Keyword(S): arrangement(s)

Combination?

Number of different ways that a certain number of objects as a group can be SELECTED from a larger number of objects.

• Order does not matter, as unordered group/list.
• Keywords: choice, selection, election.

Note: 0! = 1. there is no zero in factorial function

MathsIsFun.(2014) combinatorics: combinations-permutations. Retrieved from https://www.mathsisfun.com/combinatorics/combinations-permutations.html

Retrieved from Sir Habir, Lecturer of Cosmopolitan College of Commerce & Technology. (2016), Permutation & combination.

Measures of Dispersion (Variance & Standard Deviation)

Note: Find µ first 

Keys:

Ungrouped data

S = Summation Notation (sum of…)

c = the value of the data set

µ = the mean of the data set

n = the number of data points 

Grouped data

S = Summation Notation (sum of…)

fi = Frequency

mi = Midpoint

µ = the mean of data set

n = Sum of frequency

Example 1 (Ungrouped data)

The Maths test scores of five students are: 92, 88, 80, 68 and 52. Find the variance and standard Deviation.

Example 2 (Grouped data)

Find the Variance and Standard Deviation.

Retrieve from Sir Rodelin and Sir Habir (2015-2016). Lecturer of Cosmopolitan College of Commerce & Technology

Measures of Dispersion (Range, Quartile and Box & whisker plot)

Measures of Dispersion

•          Used to quantity the spread of the data
•          The measures of dispersion are:

1.       Range

2.       Quartile

3.       Box & Whisker

4.       Variance

5.       Standard Deviation

Range?

Range is the difference between the highest and lowest.

Example 1

76, 45, 83, 68, 63. Find the Range.

Example 2

39, 19, 9, 29, 49, 59, 49. Find the Range.

Quartiles, Interquartile range and Semi Interquartile range

•        Quartiles is the spread of a data set by breaking the data set into quarters which we have to find first quartile (Q1), second quartile (Q2) and third quartile (Q3).
•          Interquartile range is the difference between the highest quartile (Q3) and the lowest quartile (Q1).
•         Semi Interquartile range is the half of Interquartile range.

Note: arrange the data set from lowest number to highest number.

Example 1

4, 10, 6, 1, 15, 3, 2, 1, 8. Find the; 1. Quartiles

                                                        2. Interquartile range

                                                        3. Semi Interquartile range

                                                         4. Construct a Box & whisker plot

References:

Lund Research Ltd.(2013) Laerd statistics. https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php

Retrieve from Sir Habir, Mathematics lecturer, (2016)

Measures of Central Tendency (Median and Mode)

Continue of median and mode~ 

Median?

The median is middle value of a set of data. Median can be odd or even.

Example 1:

Suppose that there are two class tests and the test scores are below.

Find the media.

Test 1: 80, 90, 25, 30, 60

Test 2: 30, 45, 80, 90, 20, 50

Mode?

The mode is the value that is most often. It can be more than one mode which called multi-modal.

Example 1:

What is mode for this two set of data.

Set 1: 6, 3, 4, 6, 7, 8, 9      Set 2: 10, 20, 30, 40, 20, 20, 10, 50, 10

Example 2:

The employees of a local manufacturing plant pledged the following donations, in dollars to the United Fund: 10, 40, 25, 5, 20, 10, 50, 30, 10, 5, 15, 25, 50, 10, 30, 5, 25, 45, and 15. Treating the data as a population, calculate the mode.

*arrange the number from low to high, so easy for you to see the same number(often)

References:

Global Higher Education, (2005). C0002 Mathematics (1st ed.). Singapore: Informatics Holding Ltd, 12 Science Centre Road.

Exercises in Measures of Central Tendency

Measures of Central Tendency (Mean)

Hello guys!! This is my first topic for learn math. It just a simple formula and easy to understand but we have to understand the meaning first.

What is Measures of Central Tendency?

-          It is about the finding Triple M which is Mean, Median and Mode.

Mean?

The mean (Average) is sum of all the values in set of data then, divide into the total of values in set of data.

Formula of  Mean

Example 1: (Individual data)

The number of Distinction students on a mathematics test for 6 topics were recorded as follows:

6, 4, 2, 5, 1, 0. Find the mean.

Example 2: (Grouped data)

The number of cases per year and the mean of days of in-patients at a RIPAS hospital are tabulated below. What is the overall mean number of days per patients?

Ward	Mean no. of days	No. of cases
Surgical	20	180
Medical	16	237
Maternity	15	96
Children	14	68

References:
Lund Research Ltd.(2013) Measures of Central Tendency. https://statistics.laerd.com
Minitab Lnc.(2016) Measures of Central Tendency.
Exercises for Measures of Central Tendency

to be continue... (Median & Mode)

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