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)

Welcome to My Blog!!! :)