This document discusses measures of dispersion, or variability, in data sets. It provides examples of the times of two athletes, Ana and Josefa, in five races each. While their average times are equal at 61.6 seconds, it notes that additional measures of dispersion are needed to determine which athlete is more consistent. These measures include range, mean deviation, variance, and standard deviation. Calculating these measures will help determine which athlete's data is more homogeneous or heterogeneous, and thus which athlete the coach should choose.

1. ESTADISTICA
MEDIDAS DE
DISPERSIÓN
3° MEDIO

2. Medidas de Dispersión
Resultados de Ana
N° carrera Tiempo(s)
1 64
2 58
3 68
4 62
5 56
Resultados de Josefa
N° carrera Tiempo(s)
1 69
2 63
3 65
4 50
5 70
Utilizando las medidas centrales ¿Cuál crees debe ser la elegida?
→ 𝒙 =
64 + 58 + 68 + 62 + 56
5
=
308
5
= 61,6
→ 𝒙 =
69 + 54 + 65 + 50 + 70
5
=
308
5
= 61,6

3. Ana → 𝒙 =
64+58+68+62+56
5
=
308
5
= 61,6
Josefa→ 𝒙 =
69+54+65+50+70
5
=
308
5
= 61,6
Dado que sus
promedio son
iguales, ¿A quién
debe elegir el
entrenador?
Para ello calcularemos las medidas de
Dispersión; nos permiten conocer que tan
dispersos se encuentran los datos. Es decir si
el grupo es homogéneo o heterogéneo.
Las medidas de dispersión son:
Rango, Desviación media,
Varianza y Desviación típica.

4. Medidas de Dispersión
1
2
𝑹𝟏 = 68 − 56 = 12
Rango
Desviación media
¿Cuanto se aleja el menor del mayor de datos?
Ana
N° (s)
1 64
2 58
3 68
4 62
5 56
Josefa
N° (s)
1 69
2 63
3 65
4 50
5 70
𝑹𝟐 = 70−50 = 20
Cuanto varían, en promedio, los datos de una distribución con
respecto a la media (o promedio)
Tiempo(s) x 64 58 68 62 65
Dm 𝒙 − 𝒙 0,6 -5,4 4,6 -1,4 1,6
Tiempo(s) x 69 63 65 50 70
Dm 𝒙 − 𝒙 0,6 -5,4 4,6 -1,4 1,6

5. 4
5
varianza
Desviación típica
Ana
N° (s)
1 64
2 58
3 68
4 62
5 56
Josefa
N° (s)
1 69
2 63
3 65
4 50
5 70

6. INTRODUCTION
TO CALCULUS
1
You can enter a subtitle here if you need it

7. Do you know what helps you make your point
clear? Lists like this one:
● They’re simple
● You can organize your ideas clearly
● You’ll never forget to buy milk!
And the most important thing: the audience
won’t miss the point of your presentation
RESEARCH METHODS

8. AXIOMATIC
PROBABILITY THEORY
PROBABILITY
Mercury is the
closest planet to the
Sun and the
smallest of them all
EXPERIMENTAL
Venus has a
beautiful name and
is the second planet
from the Sun
Despite being red,
Mars is actually a
cold place. It’s full of
iron oxide dust

9. RESEARCH METHODS
DESCRIPTIVE
Mars is actually a
very cold place
CORRELATIONAL
Neptune is very far
from the Sun
CAUSAL
Jupiter is the biggest
planet of them all
EXPERIMENTAL
Saturn is a gas giant
and has rings

10. AUTOMATION
Neptune is very far
from the Sun
Mercury is the
smallest planet
COMPUTER SCIENCE
ALGORITHMS
Mars is actually a
very cold place
Earth is the only
planet with rings
PROGRAMMING
Saturn is the only
planet with rings
INFORMATION
COMPUTATION
DATABASES
Jupiter is the biggest
planet of the System

11. AWESOME
WORDS

12. “This is a quote. Words full of
wisdom that someone
important said and can make
the reader get inspired.”
—SOMEONE FAMOUS

13. A PICTURE IS WORTH
A THOUSAND WORDS

14. A PICTURE ALWAYS
REINFORCES THE CONCEPT
Images reveal large amounts of data, so
remember: use an image instead of a long
text. Your audience will appreciate it

15. 4,498,300,000
Big numbers catch your audience’s attention

16. is Jupiter's rotation period
24h 37m 23s 333,000
Earths is the Sun’s mass
386,000 km
is the distance between Earth and the Moon

17. STATISTICAL METHODS
It’s the closest planet
to the Sun and the
smallest in the System
MERCURY VENUS
Venus has a beautiful
name and is the second
planet from the Sun
MARS
Despite being red,
Mars is actually a cold
place full of iron oxide
10% 50% 75%

18. DESKTOP SOFTWARE
You can replace the image on the
screen with your own work. Just
right-click on it and select
“Replace image”

19. TABLET APP
You can replace the image on the
screen with your own work. Just
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20. MOBILE WEB
You can replace the image on the
screen with your own work. Just
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21. OUR ACTUARIAL PROFESSORS
SOFIA HILL
You can talk a bit
about this person here
PETER HARRIS
You can talk a bit
about this person here

22. VENUS
MARS
OUR EDUCATIVE CENTERS
It has a beautiful
name, but it’s hot
Despite being red,
Mars is a cold place

23. Mars is a very
cold planet
METHOD OF INVESTIGATION
PLAN
Venus has high
temperatures
DATA
Mercury is the
smallest planet
ANALYSIS VERIFICATION
Jupiter is the
biggest planet
01 02 03 04

24. RESEARCH METHODS
Despite being red, Mars is a very cold
planet full of iron oxide dust
ANALYSIS
Mercury is the closest planet to the
Sun and the smallest of them all
ENROLLMENT
Venus has a beautiful name and is
the second planet from the Sun
SUBJECTS

25. ACTUARIAL TABLE
INTERVAL
TIME
NUMBER
INTERVAL
NUMBER
CENSORED
NUMBER
EXPOSED TO RISK
DESCRIPTION
INFORMATION
0 375 12 359
Jupiter is the
biggest planet
5 362 36 344
Mars is a very
cold planet
10 323 23 311
Venus is the
smallest planet

26. BUSINESS FINANCE STATISTICS
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
25%
Mercury is the
smallest planet
25%
Despite being red,
Mars is very cold
Venus
25%
Venus has high
temperatures
25%
Jupiter is the
biggest planet
Jupiter Mercury Mars

27. STATISTICS FOR SCIENTISTS
2
You can enter a subtitle here if you need it

28. EXAMS CALENDAR
MON TUE WED THU FRI SAT SUN
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31
VENUS
Venus has high
temperatures
JUPITER
Jupiter is the
biggest planet
MARS
Mars is a very
cold planet

29. MARS
MERCURY
A GRAPH WITH DATA
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
Despite being red,
Mars is very cold
It’s the closest
planet to the Sun

30. ORGANIZATION CHART
Despite being red,
Mars is a cold place
Venus is the second
planet from the Sun
Saturn is a gas
giant with rings
ATTENDEE
PROFESSOR
ATTENDEE

31. DISCRETE MATHEMATICS
Mercury is the closest planet to the Sun and the
smallest one in the Solar System—it’s only a bit
larger than the Moon

32. COMPUTER SCIENCE I
SOFTWARE
Jupiter is the
biggest planet
HARDWARE
Neptune is very
far from the Sun
Mercury is the closest planet to the Sun
and the smallest one in the Solar System

33. ABOUT MICROECONOMICS
DEMAND
Jupiter is the
biggest planet
UTILITY
Despite being red,
Mars is very cold
SUPPLY
Neptune is very
far from the Sun

34. ABOUT THE MACROECONOMICS
SUPPLY-SIDE
Venus has a
beautiful name
MONETARY
Despite being red,
Mars is a cold place
FISCAL
Jupiter is the biggest
planet of them all

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