The document outlines the objectives and basic concepts of statistics for first-year secondary education students. It covers definitions of data types, how to create frequency tables, and calculate statistical parameters like mode, median, mean, and range. Additionally, it introduces visual representation of data through bar and pie charts.

1. STATISTICS
Subject: Mathematics
Level: First Year of Secondary Education
by Rocío Yuste Mieres

2. Objectives:
 Understand “What is Statistics for?”
 Understand and learn the different types of data:
Qualitative and Quantitative (Discrete and Continuous)
 Understand and make the Frequency table
 Understand and work out Statistical Parameters:
Mode, Median, Mean and Range
 Introduction:
Bar and Pie charts

5. Population

6. Population Sample

7. Population Sample
Data

8. “They have brown hair”
(descriptive words)

9. “They have brown hair”
(descriptive words)

10. “They have brown hair”
(descriptive words)

11. Breakfast

12. What brand?
Breakfast

13. What brand?
Qualitative
Breakfast

14. What brand?
Qualitative
How many toasts?
Breakfast

15. What brand?
Qualitative
How many toasts?
Discrete
Quantitative
Breakfast

16. What brand?
Qualitative
How many toasts?
Discrete
Quantitative
Amount of milk (ml)?
Breakfast

17. What brand?
Qualitative
How many toasts?
Discrete
Quantitative
Amount of milk (ml)?
Continuous
Quantitative
Breakfast

18. What brand?
Qualitative
How many toasts?
Discrete
Quantitative
Amount of milk (ml)?
Continuous
Quantitative Coffee or hot chocolate?
Breakfast

19. Breakfast
What brand?
Qualitative
How many toasts?
Discrete
Quantitative
Amount of milk (ml)?
Continuous
Quantitative Coffee or hot chocolate?
Qualitative

20. Raw data

21. Statistics help us…
 to collect
 to analyse
 to present
 to interpret
… data.

22. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
science
data
sample population
individual
characteristicStatistics
value
set
members

23. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
data
sample population
individual
characteristicStatistics
value
set
members

24. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample population
individual
characteristicStatistics
value
set
members

25. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample population
individual
characteristic
value
set
members

26. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample population
individual
characteristic set
members

27. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample population
individual
set
members

28. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample population
individual
members

29. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample
individual
members

30. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample
members

31. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.
sample

32. The science related to the collection, analysis, presentation and
interpretation of data is called Statistics. A statistic is a single
valuethat gives information about a characteristicstudied in a set
of individuals called population.
When it is very expensive to study the characteristic in every individualof
the population or it takes too much time, you can study it only in some
membersof the population. This set of members is called sample.

33. RAW DATA
FREQUENCY TABLE
Diagrams
Work out
Median Mean
Mode Range
Visualise
Parameters
Draw conclusions
Organise
PIE AND BAR CHARTS

34. xi fi ni Fi Xi · fi αi
N = ∑ ni = 1 ∑ xi · fi = ∑ αi = 360°
FREQUENCY TABLE
Xi : variable (characteristic)
fi : absolute frequency ni : relative frequency (fi / N)
Fi : cumulative frequency αi : angle of each sector to draw the
Pie Chart (ni · 360°)
N: size of the population or sample (∑ fi)

35. xi fi ni Fi Xi · fi αi
5 12 12 60
6 27
7 10 37
8 48
N = ∑ ni = 1 ∑ xi · fi = ∑ αi = 360°
FREQUENCY TABLE
Xi : variable (characteristic)
fi : absolute frequency ni : relative frequency (fi / N)
Fi : cumulative frequency αi : angle of each sector to draw the
Pie Chart (ni · 360°)
N: size of the population or sample (∑ fi)
How much time your neighbours spend having their breakfast
(in minutes)

36. xi fi ni Fi Xi · fi αi
5 12 12 60
6 27
7 10 37
8 48/8 = 6 48
N = ∑ ni = 1 ∑ xi · fi = ∑ αi = 360°
FREQUENCY TABLE
Xi : variable (characteristic)
fi : absolute frequency ni : relative frequency (fi / N)
Fi : cumulative frequency αi : angle of each sector to draw the
Pie Chart (ni · 360°)
N: size of the population or sample (∑ fi)
How much time your neighbours spend having their breakfast
(in minutes)

37. xi fi ni Fi Xi · fi αi
5 12 12 60
6 27–12 = 15 27
7 10 37
8 6 48
N = ∑ ni = 1 ∑ xi · fi = ∑ αi = 360°
FREQUENCY TABLE
Xi : variable (characteristic)
fi : absolute frequency ni : relative frequency (fi / N)
Fi : cumulative frequency αi : angle of each sector to draw the
Pie Chart (ni · 360°)
N: size of the population or sample (∑ fi)
How much time your neighbours spend having their breakfast
(in minutes)

38. xi fi ni Fi Xi · fi αi
5 12 12 60
6 15 27
7 10 37
8 6 37+6=43 48
N = ∑ ni = 1 ∑ xi · fi = ∑ αi = 360°
FREQUENCY TABLE
Xi : variable (characteristic)
fi : absolute frequency ni : relative frequency (fi / N)
Fi : cumulative frequency αi : angle of each sector to draw the
Pie Chart (ni · 360°)
N: size of the population or sample (∑ fi)
How much time your neighbours spend having their breakfast
(in minutes)

39. xi fi ni Fi Xi · fi αi
5 12 0,28 12 60 100,8
6 15 0,35 27 90 126
7 10 0,23 37 70 82,8
8 6 0,14 43 48 50,4
N = 43 ∑ ni = 1 ∑ xi · fi = 268 ∑ αi = 360°
FREQUENCY TABLE
Xi : variable (characteristic)
fi : absolute frequency ni : relative frequency (fi / N)
Fi : cumulative frequency αi : angle of each sector to draw the
Pie Chart (ni · 360°)
N: size of the population or sample (∑ fi)
How much time your neighbours spend having their breakfast
(in minutes)

40. MOST
AVERAGE
DIFFERENCE
MIDDLE
STATISTICAL PARAMETERS

41. MOST
AVERAGE
DIFFERENCE
MIDDLE
STATISTICAL PARAMETERS

42. MOST
AVERAGE
DIFFERENCE
MIDDLE
STATISTICAL PARAMETERS

43. MOST
MIDDLE
AVERAGE
DIFFERENCE
STATISTICAL PARAMETERS

44. MOST
MIDDLE
AVERAGE
DIFFERENCE
STATISTICAL PARAMETERS

45. MOST
MIDDLE
AVERAGE
DIFFERENCE
STATISTICAL PARAMETERS

46. MOST
MIDDLE
AVERAGE
DIFFERENCE
STATISTICAL PARAMETERS

47. MOST
MIDDLE
AVERAGE
DIFFERENCE
STATISTICAL PARAMETERS

48. xi fi ni Fi Xi · fi αi
5 12 0,28 12 60 100,8
6 15 0,35 27 90 126
7 10 0,23 37 70 82,8
8 6 0,14 43 48 50,4
N = 43 ∑ ni = 1 ∑ xi · fi = 268 ∑ αi = 360°
FREQUENCY TABLE
How much time your neighbours spend having their breakfast
(in minutes)

49. xi fi ni Fi Xi · fi αi
5 12 0,28 12 60 100,8
6 15 0,35 27 90 126
7 10 0,23 37 70 82,8
8 6 0,14 43 48 50,4
N = 43 ∑ ni = 1 ∑ xi · fi = 268 ∑ αi = 360°
FREQUENCY TABLE
How much time your neighbours spend having their breakfast
(in minutes)
mode = 6

50. xi fi ni Fi Xi · fi αi
5 12 0,28 12 60 100,8
6 15 0,35 27 90 126
7 10 0,23 37 70 82,8
8 6 0,14 43 48 50,4
N = 43 ∑ ni = 1 ∑ xi · fi = 268 ∑ αi = 360°
FREQUENCY TABLE
How much time your neighbours spend having their breakfast
(in minutes)
mode = 6
median = 6 22nd value 21 values21 values

51. xi fi ni Fi Xi · fi αi
5 12 0,28 12 60 100,8
6 15 0,35 27 90 126
7 10 0,23 37 70 82,8
8 6 0,14 43 48 50,4
N = 43 ∑ ni = 1 ∑ xi · fi = 268 ∑ αi = 360°
FREQUENCY TABLE
How much time your neighbours spend having their breakfast
(in minutes)
mode = 6
mean = 268 / 43 = 6,23
median = 6 22nd value 21 values21 values

52. xi fi ni Fi Xi · fi αi
5 12 0,28 12 60 100,8
6 15 0,35 27 90 126
7 10 0,23 37 70 82,8
8 6 0,14 43 48 50,4
N = 43 ∑ ni = 1 ∑ xi · fi = 268 ∑ αi = 360°
FREQUENCY TABLE
How much time your neighbours spend having their breakfast
(in minutes)
mode = 6
mean = 268 / 43 = 6,23
range = 8 – 5 = 3
median = 6 22nd value 21 values21 values

53. BAR CHART
How much time your neighbours spend having their breakfast
(in minutes)
0
2
4
6
8
10
12
14
16
5 6 7 8
Frequency
Minutes

54. PIE CHART
What your neighbours eat for breakfast
TOAST CAKE BISCUITS CROISSANT CORNFLAKES

55. STATISTICS
Subject: Mathematics
Level: First Year of Secondary Education
by Rocío Yuste Mieres