Topic 1: Measure of Central Tendency with Exercises

What is the measure of central tendency?

A measure of central tendency is a summary details of measurement that attempts to describe a whole set of data with a single value that represents the middle of center of its distribution.

The 3 types of measure of central tendency are:

• MODE
• MEDIAN
• MEAN

MODE

Most common occurring value in a distribution.

Example 1:

Example values: 1, 2, 3, 4, 5, 5, 5

The most common number is 5

Example 2:

Example values: 101, 101, 101, 102, 103, 104, 105,106

The most common number is 101

Example 3:

Example values: 9, 8, 4, 5, 4, 4, 3, 2, 7,1, 6

The most common number is 4.

MEDIAN

Middle value that arranged in ascending or descending order.

Example:

The median divides the distribution in half. In a distribution with and odd numbers of observations, the median is the middle value, which is 57;

51 52, 53, 54, 55, 56, 57, 58, 59

When the distribution has an even number of observations, the median value is the mean of the two middle values. In the following distribution median equals is 55.

Example 1:

Example values: 1, 3, 3, 6, 7, 8, 9

The median is 6

Example 2:

Example values: 1, 2, 3, 4, 5, 6, 8, 9

The median is 4 and 5

So, 4 +5 = 9

= 9

   2

=4.5

The answers is 4.5

Example 3:

Example values: 1, 3, 3, 5, 5, 5, 6,, 8, 9

The median is 5 and 5

So, 5 +5 = 10

= 10

   2

=5

The answers is 5

MEAN

The total sum of each value that can divide by the number of observations. 

Also known by Arithmetic average.

Example 1:

56 + 35 + 45 + 67 + 12 +24 +48 + 55+ 58 + 30

= 430

= 430

   10

= 43

Example 2:

3 + 3 + 4 + 4 + 8 + 8 + 8 + 10 + 12 + 20

= 88

=88

  10

= 8

Example 3:
9 + 10 + 12 + 12 + 10 + 11 + 12 + 13 + 16 + 38

= 143

=143

   10

= 14.3

Here is sample video of the measure of tendency:

-EXERCISE-
! GOOD LUCK!

1. What are the mean of 2, 4, 6, and 8?
2. What is the mode of 21, 4, 3, 0, 2, 4, 4, and 8?
3. What is the median of  4, 6, 8, 10, 12, 16, 17?

Topic 3: Probability with Exercises

What is Probability?
Probability mentioned in one thing happen,
Many events cannot be foreseen with total certainty. the simplest we are able to say is however probably they're to happen, victimization the concept of chance.

TOSSING A COIN: 

When a coin is tossed, there are two possible outcomes: ·         heads (H) or ·         tails (T) We say that the probability of the coin landing H is 1                                                              2 And the probability of the coin landing T is 1                                                    2 THROWING A DICE: When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6. The probability of any one of them is 1/6. In general: Probability of an event happening = Number of ways it happens                                                                 Total number of outcomes Example 1: There are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked? Number of ways it can happens: 4 (there are 4 blues) Total number of outcomes: 5 (there are 5 marbles in total) So the probability =  4                                    5                             = 0.8 Example 2: A die is rolled, find the probability that an even number is obtained. Solutions: Let us first write the sample space S of the experiment.  S = {1,2,3,4,5,6}  Let E be the event "an even number is obtained" and write it down.  E = {2,4,6}  We now use the formula of the classical probability.         P(E) = n(E)                     n(S)             = 3                       6                    = 1                       2  Example 3: Two coins are tossed find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tails). Solutions: The sample space S is given by.  S = {(H,T),(H,H),(T,H),(T,T)}  Let E be the event "two heads are obtained".  E = {(H,H)}  We use the formula of the classical probability.      P(E) = n(E)                   n(S)                   =  1                      4 Here is the sample of video: -EXERCISE- !GOOD LUCK! Question 1:  A dice is thrown once. What is the probability that the score is a factor 6? a) 1/6 b) 1/2 c) 2/3 d) 1 Question 2: The diagram shows a spinner made up of a piece of card in the shape of a regular pentagon, with a toothpick pushed through its center. The five triangles are numbered from 1 to 5.  The spinner is spun until it lands on one of five edges of the pentagon. What is the probability that the number it lands on is odd? a) 1/5 b) 2/5 c) 1/2 d) 3/5 Question 3: A card is chosen at random from a deck of 52 playing cards. There are 4 Queens and 4 Kings in a deck of playing cards. What is the probability the card chosen is a Queen or a King? a) 1/13 b) 2/13 c) 1/8 d) 2/11