Indices 2 (Exercise)

Note: If you haven't read my post about how to solve indices, you should check it now!

Here are some exercise on indices. Try to solve them before checking the solutions! I wish you luck.

Exercise




Solution

INDICES

Indices are useful in simplifying large number. You need to understand the concept of statistics.

Objectives:

– To understand the terms: square number, cube number, square and cube root. 
– To learn and use square numbers up to 225.
– To know and be able to use the index laws. 
– To be able to add, subtract, multiply and divide negative numbers.
– To be able to use powers with negative numbers.

Indices Law



Example Question

Statistical Representation 2

Here are some exercise for the Statistical Representation. You should be able to do it now. Good luck!

Questions

1) A computer shop are selling gaming equipment. In 2010, they sold 56 keyboards for $31 each, 76 mouse for $42 each, 23 headset for $19 each and 29 mousepad for $10 each. Your tasks are to :-

1. Draw a Histogram to show the difference incomes they gained for each equipment.
2. Draw a Bar Graph the total amount of gaming equipment sold. 

2) 20 students from elementary school were asked for their favorite fruits. 6 Student answered strawberry, 4 students chose Melon, 1 student love Pineapple. Another 4 students chose Pear and the rest pick banana as their favorite. You are required to draw a Pie Chart and Histogram to show the difference amount votes for each fruits.

Solutions 

1)

1.
 
2.


2)

Statistical Representation

Statistical Representation is about statistics and representing something. Well in this case, it is representing data that has been summarized from large number of data. Basically graph, charts and plots mean essentially the same.  Each types of graph represent different data. Here are some types of the graph :-

1. Bar Graph
2. Histogram Graph
3. Pie Chart

Bar Graph

Bar graph is a graph that rectangular bars are needed to represent different values for comparing groups.

Steps to draw a bar graph 

1. Draw a x-axis and y-axis   -  (x-axis is the horizontal line and y-axis is the vertical line)
2. Label the x-axis and its title - The compared groups name (E.g. Cars company, months and mobile brands)
3. Label the y-axis and its title - Numbered value. It is best to number it by even numbers suitable for your amount data (E.g. 5, 10, 15, 20, 25, 30)
4. Draw your bars - Draw a rectangular bars to tell the amount of the compared groups

Example: In 2016, Nissan Motor Co., Ltd. sold 23 cars, Toyota Motor Corporation sold 45 cars, Honda Motor Co., Ltd. sold 18 cars and Hyundai Motor Company sold 27 cars. Draw a bar graph representing total amount of cars sold from each different company.

Histogram Graph

Histogram is a pretty much the same as the bar graph but there is no gap between the bar and it is used for distribution of data.

Example: In 2016, Nissan Motor Co., Ltd. sold 23 cars, Toyota Motor Corporation sold 45 cars, Honda Motor Co., Ltd. sold 18 cars and Hyundai Motor Company sold 27 cars. Draw a Histogram representing total amount of cars sold from each different company.

Pie Chart

Pie chart is a round chart divided into sectors. It is always measured in angle (Degree). The maximum angle is 360.

Example: In 2016, Nissan Motor Co., Ltd. sold 23 cars, Toyota Motor Corporation sold 45 cars, Honda Motor Co., Ltd. sold 18 cars and Hyundai Motor Company sold 27 cars. Draw a Pie Chart representing total amount of cars sold from each different company.

Probability 2

Tree Diagram - To list the probability of possible outcomes.

Example Question

There are one Geography(GP) book and three Principle of Account(POA) books on the book shelf. Kim selects two books at random, one book after another. 

1) Draw a probability tree diagram for the possible outcome




2) Two Principle Of Account Book




Answer = ½

3) One book of Principle Of Account and Geography



Answer = ¼

Probabilty

Probability - The measure of how likely an event are about to happen.
Experiment - A situation involving chances/probability than leads to results called outcome
Outcome/Sample point - The result of a single trial of an experiment
Event/Sample space - All the possible outcome of an experiment

Example Questions

A bag consist of 30 heart candies with numbered sticker from 1 to 30. A candy is drawn at random and its numbered is noted. What is the probability that the candy drawn:-

a) Has an odd number on it?


Answer = 15 numbers : 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29.


b) Has a number that is divisible by 5?


Answer = 6 numbers : 5, 10, 15, 20, 25 and 30.


c) Has a number that is divisible by 3 and 4?



Answer = 16 numbers : 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28 and 30.

Measures of Dispersion 2

Variance

- The average of the squared differences from the mean.

Standard Deviation

- Measurement of how spread out numbers are. Its is the square root of the variance.

There are two (2) types of formula for standard deviation :-
(1) Standard Deviation - Population             (2) Standard Deviation - Group

Standard Deviation (Population)    - Are always used for individual data.
Standard Deviation (Group)           - Always use the total frequency for finding variance.


Formula symbol keyword:






Steps to do the formula :-

1) Find the mean of the data/numbers
2) Subtract each number with the mean(from step 1) and square the answer
3) Find the mean of the answer(from step 2)
4) Square root the answer(from step 3) - Depends on the question requirement (Standard Deviation)

Example Question

Question = 1,4,14,1,14,1

Step 1
 Find the mean of the data/numbers



Step 2
Subtract each number with the mean(from step 1) and square the answer



Step 3
Find the mean of the answer(from step 2)



Step 4 
Square root the answer(from step 3) - ONLY CALCULATE WHEN THE QUESTION ASK! (Standard Deviation)



~Working Finish~

Measures of Dispersion

What is Mean?
- The average value of the data

What is Median?
- The middle number of the data. Some data need to be change first from the lowest to the highest (Ascending).

What is Mode?
- The repeating data or data that occur the most.

What is Range?
- The highest value of the data subtract with the lowest value of the data.

Example of Mean, Median, Mode and Range

14,1,14,1,14,13,20

From the data above, Find the:
a. Mean
b. Median
c. Mode
d. Range

Permutation and Combination Multiplication rule and Exercise

Permutation and Combination Multiplication Rule

Example:   A NBA Basketball team, Phoenix Sun roster consist of six Guards, four Fowards and three Centers. In how many ways can the coach select a starting line up of two guards, two Fowards and one Center?




Permutation and Combination Exercise

1) In sport house of 24 students, a first and second prize are to be awarded. In how many                      different ways can this be done?

2) In a room of 20, 12 are girls and the rest are boys. A student body of 2 prefects are to be                    elected. How many ways can they be chosen if:

    a. Both prefects elected are girls
    b. Both prefects elected are boys
    c. 1 girl and 1 boy prefects

3) A fan club has 28 members. In how many ways can the president, web-designer and admin            be chosen to form a committee of three?

4) In how many ways can a football team of 11 players be chosen from 30 people?

5) In how many ways can a committee of 7 be chosen from 9 office pairs if:

a. The committee must have 3 men and 4 women
b. No restriction are made
c. The committee are all elected by men

Permutation and Combination

PERMUTATION AND COMBINATION

Permutation   :      Certain number of objects that can be arrange in order from a large number of objects in different number of ways.
                              It is an ordered group/list or an order is important.
Keyword         :      Arrangement

Combination   :     Certain number of objects in a group that can be selected from a large number of objects in different number of ways.
                             It is an un-ordered group/list
Keyword         :     Selection, Election, Choice


FORMULA

Key:-                 n = Number selected     N = Total number     ! = Factorial     

Permutation   :

                                    

Example: How many ways can you arrange these 5 objects?



n = none     N = 5






Combination   :

                                  

Example: How many can you arrange these 5 fruits picking 3 at a time?



n = 3     N = 5





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