Data Handling
Learning Outcomes

Understand terms: sample, population, discrete, continuous and variable

Understand the need for different sampling techniques including random and stratified sampling and be able to generate random numbers with a calculator or computer to obtain a sample

Be able to design a questionnaire (taking bias into account)

Understand the need for grouping data and the importance of class limits and class boundaries when doing so

DH - Collecting Data
Data Handling
Sample:
A sample is a subset of the population. 11A would be a subset of the following populations → year 11, senior pupils, pupils of St Mary’s
Population:
The total number of individuals or objects being analyzed; this quantity is user defined. E.g. pupils in a school, people in a town, people in a postal code.
Discrete:
A discrete variable is often associated with a count, they can only take certain values – usually whole numbers.
E.g. number of children in a family, number of cars in a street, number of people in a class.

DH - Collecting Data
Data Handling
Continuous:
A continuous variable is often associated with a measurement, they can take any value in given range.
E.g. height, weight, time.
Variable:
See discrete & continuous above.

DH - Collecting Data
Data Handling
Random Sampling:
In simple random sampling every member of the population is a given number. If the population has 100 member , they will each be given a number between 000 and 999 (inclusive) then 3 digit random numbers are used to select the sample (ignore repeats)
Stratified Sample:
Often data is collected in sections (strata).
Eg. Number of pupils in a school. In selecting such a sample data is taken as a proportion of the total population. Here we should sample twice as many people in year 10 than in year 8.
Year No. of Pupils
8 100
9
10
11
12
Total
50
200
200
150
700

DH - Collecting Data
Data Handling
Stratified Sample:
Year
8
9
10
11
12
To obtain as sample of 70 pupils out of the 700, we construct the following table
No. of
Pupils
100
50
200
200
150
700
Proportion of total No. of pupils to be sampled
100
50
/
700
/
700
200 /
200
/
150
/
700
700
700
=
1
/
=
1
=
3
/
14
= 2 /
=
2
/
7
7
7
/
14
100
/
700
=
1
/
7
× 70 = 10
100
/
700
=
1
/
14
× 70 = 5
100 /
700
= 2 /
7
× 70 = 20
100
/
700
=
2
/
7
× 70 = 20
100
/
700
=
3
/
14
× 70 = 15
70

DH - Collecting Data
Questionnaires
1. Sample should represent population
2. Sample must be of a reasonable size to represent population
(at least 30) sample mean = population mean
3. Questions should: i) be as short as possible ii) use tick boxes iii) avoid bias iv) avoid leading questions

Additional Notes

Data Handling
Understand terms: sample, population, discrete, continuous and variable
Understand the need for different sampling techniques including random and stratified sampling and be able to generate random numbers with a calculator or computer to obtain a sample
Can Revise
Do Further
 
 
Be able to design a questionnaire (taking bias into account)
Understand the need for grouping data and the importance of class limits and class boundaries





Data Handling
Learning Outcomes

Understand that in order to gain a mental picture of a collection of data it is necessary to obtain a measure of average and range

Be able to determine the mean, median and mode for a set of raw scores and an ungrouped frequency table

Be able to obtain the median and interquartile range for grouped data from a cumulative frequency graph

Understand the advantages and disadvantages of each average and measure of spread

DH - Analysing Data
Mean
Sum of all measures divided by total number of measures.
x
  n x
 everyone included
× affected by extremes
Mode
Most popular / most frequent occurrence.
× not everyone included  not affected by extremes
Median
Arrange data in ascending order; the median is the middle measure. Position = ½ (n + 1)
× not everyone included  not affected by extremes

DH - Analysing Data
Examples
Calculate the Mean, Median and Mode for: a) 3, 4, 5, 6, 6, b) 2.4, 2.4, 2.5, 2.6
* Normal distribution is where the mean, median and mode are close eg example b)

DH - Analysing Data
The number of children in 30 families surveyed are surveyed.
The results are given below.
Calculate a) The mean number of children per family
(No. of children) x
(No of families) f
0
4
1
5
2
10
3
6
4
3
5
2 b) The median

DH - Analysing Data
Often data is grouped so that patterns and the shape of the distribution can be seen. Group sizes can be the same, although there are no applicable rules.
Find the mean of:
Mark
30 – 34
40 – 49
50 – 59
60 – 69
Frequency ( f )
7
14
21
9
∑ f = 51
Midpoint ( x ) fx

DH - Analysing Data
Find the median of the following grouped frequency distribution.
Cumulative
Frequency
Upper Limit Length
21 – 24
25 – 28
29 – 32
33 – 36
37 – 40
Frequency
3
7
12
6
4

DH - Analysing Data
Median = Measure of central location
Interquartile range = Measure of spread
= Q
3
– Q
1
Q
1
Q
3
= 25th percentile
= 75th percentile
Q
1
Q
2
Q
3
= ¼ (n + 1)
= ½ (n +1)
= ¾ (n +1)
= 8.25
th → 26
= 16.5
th → 30
= 24.75
th → 33
Interquartile Range = Q
3
– Q
= 33 – 26
1
= 7
Q3
Q2
Q1
Upper Limit

DH - Analysing Data

Data Handling
Can Revise
Do Further
  
Understand that in order to gain a mental picture of a collection of data it is necessary to obtain a measure of average and range

Be able to determine the mean, median and mode for a set of raw scores and an ungrouped frequency table

Be able to obtain the median and interquartile range for grouped data from a cumulative frequency graph

Understand the advantages and disadvantages of each average and measure of spread







Data Handling
Learning Outcomes

Revise drawing of pie charts, line graphs and bar charts

Be able to present data using a stem and leaf diagram, determine mean, Median and quartiles

Be able to draw a boxplot for a set of values and compare more than one box and whisker plots with reference to their average, spread, skewness

Be able to draw a histogram to represent groups with unequal widths

Know which diagram to use to represent data, the advantages and disadvantages of each type.

Be aware of the shape of a normal distribution and understand the concept of skewness

DH - Presenting Data
A box & Whisker plot illustrates: a) The range of data b) The median of data c) The quartiles and interquartile range of data d) Any indication of skew within the data
Q1 Q2 Q3
Scale

DH - Presenting Data
y
×
×
×
×
×
× ×
×
× x
Positive Correlation x
▲ y
▲ y
×× x
Negative Correlation x ▲ y ▼ y
× x
No Correlation x & y are independent

DH - Presenting Data
32 packages were brought to the local post office. The masses of the packages were recorded as follows
Mass (g)
No of packages
0 < m ≤ 30 30 < m ≤ 40 40 < m ≤ 50 50 < m ≤ 90
3 10 12 7
With unequal class widths we draw a histogram.
There are 2 important differences between a bar chart and a histogram
1. In a bar chart the height of the bar represents the frequency.
2.
In a histogram the ‘ x
’ axis is a continuous scale.

DH - Presenting Data
When the classes are of unequal width we calculate and plot frequency density
Frequency Density = Frequency
Class Width
Group
0 < m ≤ 30
30 < m ≤ 40
40 < m ≤ 50
50 < m ≤ 90
Frequency Class Width
3
10
12
7
30
10
10
40
Frequency
Density

DH - Presenting Data
When data are grouped to draw a histogram or a cumulative frequency distribution, individual results are lost. The advantage of grouping is that patterns (distribution) can be seen. In a stem and leaf diagram individual results are retained and the spread / distribution of the data can be seen.
Draw a stem and leaf diagram for the data:
10, 11, 12, 15, 23, 26, 29, 32, 33, 34, 35,36, 42, 43, 44, 56, 57
Stem
1
2
3
4
5
Leaf

DH - Presenting Data

Data Handling

Revise drawing of pie charts, line graphs and bar charts

Be able to present data using a stem and leaf diagram, determine mean, Median and quartiles

Be able to draw a boxplot for a set of values and compare more than one box and whisker plots with reference to their average, spread, skewness

Be able to draw a histogram to represent groups with unequal widths

Know which diagram to use to represent data, the advantages and disadvantages of each type.

Be aware of the shape of a normal distribution and understand the concept of skewness
Can Revise
Do Further
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