Post on 26-Jun-2015
description
transcript
April 13, 2023
Grouping Data
NextNext
3. Representing continuous data.
April 13, 2023
Sometimes data is continuous. That means it doesn't fit into distinct categories, such as shoe size, but changes gradually.Height, weight, length, time and temperature are all continuous. There is a continuous scale that can be read at an infinite number of points.
Explanation
NextNextMoreMore
If you record a measurement with a figure, such as 18 cm, it is unlikely that this is actually exact.
April 13, 2023
This credit card card is about 8 cm long…
but if we look closer…
we can see that it is 8.2 cm long…
and if we look closer still…
we see that it is 8.2 cm, and a bit more.
Explanation
NextNextMoreMore
April 13, 2023
Even when you use decimal places, you are unlikely to write an absolutely exact measurement.
So when you make any measurement, you are probably rounding it up or down, whether to a decimal place, or a whole figure.
You are in fact grouping the data at the level of accuracy you choose to use.
When you say something is ‘18 cm’, you may mean…
‘any reading equal to, or more than 17.5 cm and less than 18.5 cm’.
Explanation
NextNextMoreMore
April 13, 2023
‘any reading equal to, or more than 17.5 cm and less than 18.5 cm’.
This can be written 17.5 ≤ w < 18.5
The width of the credit card
is more than, or equal to
17.5
and less than
18.5
To make handling continuous data easier, it can be put into groups larger than a single whole number.
Explanation
NextNextMoreMore
April 13, 2023
These figures show the height in cm of 70 year 10 students at this school.
171 162 169 178 184 174 166
165 171 169 161 178 176 171
158 163 177 165 162 172 168
174 172 174 168 170 175 171
170 172 175 170 176 164 172
180 170 172 180 167 169 172
167 173 155 171 167 174 178
178 173 166 174 170 166 188
173 167 171 161 176 166 180
169 163 174 168 173 161 166
To make this data easier to use, we can group it like this.
Height (cm) Frequency
155 ≤ h < 160 2
160 ≤ h < 165 7
165 ≤ h < 170 19
170 ≤ h < 175 28
175 ≤ h < 180 9
180 ≤ h < 185 4
185 ≤ h < 190 1
You can show continuous data on a bar graph, using proper scales on both axes.
Explanation
NextNextMoreMore
April 13, 2023
You can show continuous data on a bar graph, using proper scales on both axes.
Height (cm) Frequency
155 ≤ h < 160
160 ≤ h < 165
165 ≤ h < 170
170 ≤ h < 175
175 ≤ h < 180
180 ≤ h < 185
185 ≤ h < 190 155 160 165 170 175 180 185 1900
5
10
15
20
25
30
35
Fre
quen
cy
Height (cm)
As the x axis shows a continuous scale, the bars should touch, making this a histogram.
2
7
19
28
9
4
1
Explanation
MoreMore
April 13, 2023
You can show continuous data on a bar graph, using proper scales on both axes.
Height (cm) Frequency
155 ≤ h < 160
160 ≤ h < 165
165 ≤ h < 170
170 ≤ h < 175
175 ≤ h < 180
180 ≤ h < 185
185 ≤ h < 190 155 160 165 170 175 180 185 1900
5
10
15
20
25
30
35
Fre
quen
cy
Height (cm)
As the x axis shows a continuous scale, the bars should touch, making this a histogram.
2
7
19
28
9
4
1
You can also represent this data using a frequency polygon.
You need to plot the frequency against the mid point of each group.Join the points using straight lines.Do not extend the polygon beyond your plots.
Explanation
MoreMore
April 13, 2023
You can also represent this data using a frequency polygon.As you do not know the exact value for each item of data, you can only estimate the mean of grouped data.
Do not extend the polygon beyond your plots.
Height (cm) Frequency
155 ≤ h < 160
160 ≤ h < 165
165 ≤ h < 170
170 ≤ h < 175
175 ≤ h < 180
180 ≤ h < 185
185 ≤ h < 190 155 160 165 170 175 180 185 1900
5
10
15
20
25
30
35
Fre
quen
cy
Height (cm)
2
7
19
28
9
4
1
Join the points using straight lines.
Explanation
MoreMore
April 13, 2023
Add columns for midpoint and midpoint × frequency to your table and a row for totals.As you do not know the exact value for each item of data, you can only estimate the mean of grouped data.
Height (cm) Frequency
155 ≤ h < 160
160 ≤ h < 165
165 ≤ h < 170
170 ≤ h < 175
175 ≤ h < 180
180 ≤ h < 185
185 ≤ h < 190
2
7
19
28
9
4
1
Explanation
MoreMore
April 13, 2023
Add columns for midpoint and midpoint × frequency to your table and a row for totals.
Height (cm) Frequency
155 ≤ h < 160
160 ≤ h < 165
165 ≤ h < 170
170 ≤ h < 175
175 ≤ h < 180
180 ≤ h < 185
185 ≤ h < 190
2
7
19
28
9
4
1 187.5
182.5
177.5
172.5
167.5
162.5
157.5
187.5
730
11132.5
1597.5
4312.5
3015
975
315
65
Midpoint M × F
Totals
Mean = 11132.5 ÷ 65
The mean = the total of the midpoint × frequency column divided by the total of the frequency column.
= 171.3 cm to 1d.p.
Explanation
MoreMore
April 13, 2023
The mean = the total of the midpoint × frequency column divided by the total of the frequency column.The range cannot be stated accurately, as we do not know the actual highest and lowest measure.
Height (cm) Frequency
155 ≤ h < 160
160 ≤ h < 165
165 ≤ h < 170
180 ≤ h < 185
185 ≤ h < 190
2
7
19
28
9
4
1 187.5
182.5
177.5
172.5
167.5
162.5
157.5
187.5
730
11132.5
1597.5
4312.5
3015
975
315
65
Midpoint M × F
Totals
Mean = 11132.5 ÷ 65
The modal class is the group with the highest frequency.
= 171.3 cm to 1d.p.
175 ≤ h < 180
170 ≤ h < 175
The range is estimated by taking the mid points of the highest and lowest groups.
Explanation
Range = 157.5 to 187.5EndEndMoreMoreNextNext