MTH 110 – INTRODUCTION TO
STATISTICS
Session 4 – Measures of Dispersion, Variance and Standard Deviation Instructor: Manos Takas Email: m.takas@cityu.gr

Range Look at these two sets of data: 2, 3, 4, 5, 6 3,2,3,5,13 -3,2,3,5,13 They both have a mean of 4. However, you can see that the first data set (21 is more spread out than the second data set. The mean doesn't tell you this. _ To represent the data more accurately, you need the mean plus a measure of the spread or dispersion of the data. One simple measure of dispersion is the range. The range of a set of data is the highest value minus the lowest value

In this case the range of set [1] is 6 - 2 = 4. The range of set [2] is 13 (-3) = 16. The range is easy to calculate, but there are other measures of spread that are more useful.

1

24/10/2011

Variance and Standard Deviation The mean of the deviations from the mean squared is called the variance, usually written as σ 2

The variance is calculated as:

σ2

=

1 ∑ ( x − x )2 n
2

Sometimes it is easier to calculate a variance using the alternative formula:

σ

⎛∑x⎞ 1 = ∑ x2 − ⎜ ⎜ n ⎟ ⎟ n ⎝ ⎠

2

Standard Deviation The standard deviation σ is defined as the square root of the variance

⎛ ∑ x2 ⎞ 1 1 2 σ= ∑ x − ⎜ n ⎟ = n ∑ ( x − x )2 ⎜ ⎟ n ⎝ ⎠ 2

Standard Deviation for Frequency Distributions

σ2 =

1 ∑ n

⎛ ∑ fx ⎞ fx 2 − ⎜ ⎜ n ⎟ ⎟ ⎝ ⎠

2

Where f represents the frequency of the x observation and n=Σf

...(LSCM) Sem I
Batch 2013-15
Measures of Dispersion – Comparison of Cargo shipped via Airline Vs Rail Sector for last five years
In statistics, dispersion (also called variability, scatter, or spread) denotes how stretched or squeezed is a distribution (theoretical or that underlying a statistical sample). Common examples of measures of statistical dispersion are the variance, standard...

...spertion
MEASURES OF DISPERSION
I. Meaning and Types of Measures of DispersionMeasures of Dispersion ( Variation or Spread )
- is a measure used to describe the variation of a set of data
|Measure of Dispersion |Symbol for |
| |Parameter...

...the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.
The Standard 3 class is where the transition from junior to senior level occurs where...

...
Contents
Question 1 3
Question 2a 5
Question 2b 6
Question 2c 7
Question 3a 8
Question 3b 8
Question 3c 10
Question 3d 11
Question 4 12
Question 5 14
References 15
Question 1
The sampling method that Mr. Kwok is using is Stratified Random Sampling Method. In this case study, Mr Kwok collected a random sample of 1000 flights and proportions of three routes in the sample. He divides them into...

...distribution: (3)
Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) and then we can build the F-distribution.
F statistic ():
Defined as the ratio of the dispersions of the two distributions, in other words it is the value calculated by the ratio of two sample variances . F always >=1.
The F...

...probabilities related to spending behavior might vary, depending on the gender of the respondent.
Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from:
a. [variable 4] spends at least $15 during a trip to Springdale Mall.
b. [variable 5] spends at least $15 during a trip to Downtown.
d. [variable 6] spends at least $15 during a trip to West Mall.
Comparing the preceding probabilities,...

...and the promoter?
It adds complimentary ribonucleotides and a promoter is the base sequence in the DNA that signals the start of a gene.
3. List 3 ways RNA is modified.
Addition of a 5’ cap, Addition of a 3’ poly A tail, and introns being removed.
4. What is the genetic code? What does it mean to state the genetic code is
redundant and practically universal?
Most of the code is the same for all organisms.
5. What is the difference between an anticodon and a codon?
A...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times...

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