Handling data and probability 2do ESO

1. Index Types of data Frequency Averages Exercises
Handling data and probability
Matematicas 2o E.S.O.
Alberto Pardo Milanes
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2. Index Types of data Frequency Averages Exercises
1 Types of data
2 Frequency
3 Averages
4 Exercises
Alberto Pardo Milanes Handling data and probability

3. Index Types of data Frequency Averages Exercises
Types of data
Alberto Pardo Milanes Handling data and probability

4. Index Types of data Frequency Averages Exercises
Types of data
Organizing data
Organizing data in a table can give you more information.
There are two types of data:
qualitative data which is described using words and quantitative
data which consist of numbers.
Example: Football teams, vegetables or colors are qualitative data.
Temperatures, sizes, heights are quantitative data.
Alberto Pardo Milanes Handling data and probability

5. Index Types of data Frequency Averages Exercises
Types of data
Types of quantitative data
Quantitative data can be discrete or continuous:
discrete data can only take particular values,
if it is not discrete then it is continuous.
Continuous data can not be measured exactly.
Example: Ages, sizes and numbers of siblings are discrete quan-
titative data. Temperatures, widths and heights are continuous
quantitative data.
Continuous data can be grouped into class intervals that makes it
easier to record and handle them.
Alberto Pardo Milanes Handling data and probability

6. Index Types of data Frequency Averages Exercises
Frequency
Alberto Pardo Milanes Handling data and probability

7. Index Types of data Frequency Averages Exercises
Frequency
What's the frequency?
In an experiment the frequency of a result is the number of times
it occurred.
Example: The marks gained by a group of students is...
7 6 4 6 7 8 10 5 6 5 We use a table for

8. nd-
ing the frequency fi.
Marks fi
4 1
5 2
6 3
7 2
8 1
10 1
N=10
The total number of observations is N = 10.
Alberto Pardo Milanes Handling data and probability

9. Index Types of data Frequency Averages Exercises
Frequency
What's relative frequency?
Relative frequency is the frequency expressed as a proportion: to

10. nd the relative frequency, you have to divide the frequency by the
number of observations.
Example: The marks gained by a group of students is...
7 6 4 6 7 8 10 5 6 5 We use a table for

11. nding relative frequency hi.
Marks fi hi
4 1 1/10=0.1
5 2 2/10=0.2
6 3 3/10=0.3
7 2 2/10=0.2
8 1 1/10=0.1
10 1 1/10=0.1
N=10 10/10=1
Alberto Pardo Milanes Handling data and probability

12. Index Types of data Frequency Averages Exercises
Averages
Alberto Pardo Milanes Handling data and probability

13. Index Types of data Frequency Averages Exercises
Averages
The mode is the most common value.
The mean (or average) is the sum of the values divided by the
total number of values.
Example: Tom has 23 euros, Fred has 16 euros and Mary has
21 euros. The mode of those values is 23 euros and the mean is
23 + 16 + 21
3
=
60
3
= 20 euros.
The median is the data point that is in the middle when the data
is listed in order. When there are two central values is their mean.
Alberto Pardo Milanes Handling data and probability

14. Index Types of data Frequency Averages Exercises
Exercises
Alberto Pardo Milanes Handling data and probability

15. Index Types of data Frequency Averages Exercises
Exercises
Exercise 1
The number of books read by a group of students last year is listed
below:
6 3 1 2 5 1 2 4 1 3 2 2 1 1 0
0 1 1 0 1 0 2 2 2 3 3 1 4 1 0
Complete a table for

16. nding the frequency and the relative
frequency.
Multiply relative frequency to obtain the percentages.
Calculate also the mean, the median, the mode and the range (the
dierence between the largest and smallest results in a data set).
Alberto Pardo Milanes Handling data and probability

17. Index Types of data Frequency Averages Exercises
Exercises
Exercise 2
The total number of goals scored in each of La Liga matches this
weekend were:
2 3 6 0 2 2 5 7 5 3
Illustrate these data on a pie chart.
Which number of goals was the most common?
How is it this number called?
Alberto Pardo Milanes Handling data and probability

18. Index Types of data Frequency Averages Exercises
Exercises
Exercise 3
Mayte draws the following bar chart to illustrate the ages of some
friends:
1 Create a frequency table.
2 How many of Mayte's
friends are included on
the bar chart?
3 How many of her friends
are of the age fourteen or
younger?
Alberto Pardo Milanes Handling data and probability

19. Index Types of data Frequency Averages Exercises
Exercises
Exercise 4
Here are the marks gained by 28 students in a maths' exam:
7 7 8 9 7 5 5 4 7 6 6 3 8 6
5 8 8 8 5 5 3 6 6 7 6 7 3 6
Create a frequency table and

20. nd the average mark and the mode.
Alberto Pardo Milanes Handling data and probability

21. Index Types of data Frequency Averages Exercises
Exercises
Exercise 5
This table shows the rainfall in the city of Malaga:
Month Ene Feb Mar Abr May Jun
L=m2 81 55 49 41 25 12
Month Jul Ago Sep Oct Nov Dic
L=m2 2 6 16 56 95 88
1 Draw a graph to display this information.
2 Work out the mean monthly rainfall.
Alberto Pardo Milanes Handling data and probability

22. Index Types of data Frequency Averages Exercises
Exercises
Exercise 6
The pie chart displays the percent of muscle, fat and bones in the
human body for a 80kg man.
Find the mode of the data set.
Complete a table for

23. nding
the frequency and the relative
frequency.
fi hi Percent
Muscle
Bones
Fat
Other
Alberto Pardo Milanes Handling data and probability