How to tell if there is equal variance in a box plot?
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I'm trying to decide if the variance in these groups in this boxplot are equal, so how can I tell how much variation each group has just looking at the box plot? And how can I tell if they all have equal variance?
Here is the boxplot:
statistics
asked Jun 1 '14 at 10:42
joe
49911025
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I'm trying to decide if the variance in these groups in this boxplot are equal, so how can I tell how much variation each group has just looking at the box plot? And how can I tell if they all have equal variance?
Here is the boxplot:
statistics
asked Jun 1 '14 at 10:42
joe
49911025
you can't calculate the variance from these pictures. but you can look at other measures of spread, such as the IQR and range. Honda, for example, has a smaller range and IQR than the others.
– symplectomorphic
Jun 1 '14 at 14:57
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm trying to decide if the variance in these groups in this boxplot are equal, so how can I tell how much variation each group has just looking at the box plot? And how can I tell if they all have equal variance?
Here is the boxplot:
statistics
asked Jun 1 '14 at 10:42
joe
49911025
I'm trying to decide if the variance in these groups in this boxplot are equal, so how can I tell how much variation each group has just looking at the box plot? And how can I tell if they all have equal variance?
Here is the boxplot:
statistics
statistics
asked Jun 1 '14 at 10:42
joe
49911025
asked Jun 1 '14 at 10:42
joe
49911025
asked Jun 1 '14 at 10:42
joe
49911025
asked Jun 1 '14 at 10:42
joe
49911025
asked Jun 1 '14 at 10:42
joe
49911025
49911025
you can't calculate the variance from these pictures. but you can look at other measures of spread, such as the IQR and range. Honda, for example, has a smaller range and IQR than the others.
– symplectomorphic
Jun 1 '14 at 14:57
add a comment |
you can't calculate the variance from these pictures. but you can look at other measures of spread, such as the IQR and range. Honda, for example, has a smaller range and IQR than the others.
– symplectomorphic
Jun 1 '14 at 14:57
you can't calculate the variance from these pictures. but you can look at other measures of spread, such as the IQR and range. Honda, for example, has a smaller range and IQR than the others.
– symplectomorphic
Jun 1 '14 at 14:57
you can't calculate the variance from these pictures. but you can look at other measures of spread, such as the IQR and range. Honda, for example, has a smaller range and IQR than the others.
– symplectomorphic
Jun 1 '14 at 14:57
add a comment |
1 Answer
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A boxplot illustrates the range and the interquartile range (IQR), both of which are measures of the variation in a data set. Generally the range is considered to be too easily influenced by extreme values, so the IQR is preferred.
In the data sets above, we can say the following:
Ford, Nissan, Toyota and Volkswagen have similar IQR, so have similar variation (not variance).
Honda and Mitsubishi have similar IQR to each other, which is less than that of the previous group.
You can, however, estimate the variance from a boxplot.
Let me consider the Toyota data.
We have (very roughly):
Smallest value: 400
Lower quartile: 650
Median: 850
Upper quartile: 1200
Largest value: 1500
Although we don't know the sample size, we can still construct a grouped frequency table for the data, with f=25 (25%) for each of the quarters:
interval frequency (f) mid-value (x) fx fx^2
400 to 650 25 525 13125 6890625
650 to 850 25 750 18750 14062500
850 to 1200 25 1025 25625 26265625
1200 to 1500 25 1350 33750 45562500
--------------------------------------------------------------
Totals 100 91250 92781250
These can be used to estimate the mean as 912.5 and the variance as 95156.
answered Apr 20 '15 at 23:54
tomi
6,18611132
add a comment |
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1 Answer
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1 Answer
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up vote
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A boxplot illustrates the range and the interquartile range (IQR), both of which are measures of the variation in a data set. Generally the range is considered to be too easily influenced by extreme values, so the IQR is preferred.
In the data sets above, we can say the following:
Ford, Nissan, Toyota and Volkswagen have similar IQR, so have similar variation (not variance).
Honda and Mitsubishi have similar IQR to each other, which is less than that of the previous group.
You can, however, estimate the variance from a boxplot.
Let me consider the Toyota data.
We have (very roughly):
Smallest value: 400
Lower quartile: 650
Median: 850
Upper quartile: 1200
Largest value: 1500
Although we don't know the sample size, we can still construct a grouped frequency table for the data, with f=25 (25%) for each of the quarters:
interval frequency (f) mid-value (x) fx fx^2
400 to 650 25 525 13125 6890625
650 to 850 25 750 18750 14062500
850 to 1200 25 1025 25625 26265625
1200 to 1500 25 1350 33750 45562500
--------------------------------------------------------------
Totals 100 91250 92781250
These can be used to estimate the mean as 912.5 and the variance as 95156.
answered Apr 20 '15 at 23:54
tomi
6,18611132
add a comment |
up vote
0
down vote
A boxplot illustrates the range and the interquartile range (IQR), both of which are measures of the variation in a data set. Generally the range is considered to be too easily influenced by extreme values, so the IQR is preferred.
In the data sets above, we can say the following:
Ford, Nissan, Toyota and Volkswagen have similar IQR, so have similar variation (not variance).
Honda and Mitsubishi have similar IQR to each other, which is less than that of the previous group.
You can, however, estimate the variance from a boxplot.
Let me consider the Toyota data.
We have (very roughly):
Smallest value: 400
Lower quartile: 650
Median: 850
Upper quartile: 1200
Largest value: 1500
Although we don't know the sample size, we can still construct a grouped frequency table for the data, with f=25 (25%) for each of the quarters:
interval frequency (f) mid-value (x) fx fx^2
400 to 650 25 525 13125 6890625
650 to 850 25 750 18750 14062500
850 to 1200 25 1025 25625 26265625
1200 to 1500 25 1350 33750 45562500
--------------------------------------------------------------
Totals 100 91250 92781250
These can be used to estimate the mean as 912.5 and the variance as 95156.
answered Apr 20 '15 at 23:54
tomi
6,18611132
add a comment |
up vote
0
down vote
up vote
0
down vote
A boxplot illustrates the range and the interquartile range (IQR), both of which are measures of the variation in a data set. Generally the range is considered to be too easily influenced by extreme values, so the IQR is preferred.
In the data sets above, we can say the following:
Ford, Nissan, Toyota and Volkswagen have similar IQR, so have similar variation (not variance).
Honda and Mitsubishi have similar IQR to each other, which is less than that of the previous group.
You can, however, estimate the variance from a boxplot.
Let me consider the Toyota data.
We have (very roughly):
Smallest value: 400
Lower quartile: 650
Median: 850
Upper quartile: 1200
Largest value: 1500
Although we don't know the sample size, we can still construct a grouped frequency table for the data, with f=25 (25%) for each of the quarters:
interval frequency (f) mid-value (x) fx fx^2
400 to 650 25 525 13125 6890625
650 to 850 25 750 18750 14062500
850 to 1200 25 1025 25625 26265625
1200 to 1500 25 1350 33750 45562500
--------------------------------------------------------------
Totals 100 91250 92781250
These can be used to estimate the mean as 912.5 and the variance as 95156.
answered Apr 20 '15 at 23:54
tomi
6,18611132
A boxplot illustrates the range and the interquartile range (IQR), both of which are measures of the variation in a data set. Generally the range is considered to be too easily influenced by extreme values, so the IQR is preferred.
In the data sets above, we can say the following:
Ford, Nissan, Toyota and Volkswagen have similar IQR, so have similar variation (not variance).
Honda and Mitsubishi have similar IQR to each other, which is less than that of the previous group.
You can, however, estimate the variance from a boxplot.
Let me consider the Toyota data.
We have (very roughly):
Smallest value: 400
Lower quartile: 650
Median: 850
Upper quartile: 1200
Largest value: 1500
Although we don't know the sample size, we can still construct a grouped frequency table for the data, with f=25 (25%) for each of the quarters:
interval frequency (f) mid-value (x) fx fx^2
400 to 650 25 525 13125 6890625
650 to 850 25 750 18750 14062500
850 to 1200 25 1025 25625 26265625
1200 to 1500 25 1350 33750 45562500
--------------------------------------------------------------
Totals 100 91250 92781250
These can be used to estimate the mean as 912.5 and the variance as 95156.
answered Apr 20 '15 at 23:54
tomi
6,18611132
answered Apr 20 '15 at 23:54
tomi
6,18611132
answered Apr 20 '15 at 23:54
tomi
6,18611132
answered Apr 20 '15 at 23:54
tomi
6,18611132
6,18611132
add a comment |
add a comment |
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you can't calculate the variance from these pictures. but you can look at other measures of spread, such as the IQR and range. Honda, for example, has a smaller range and IQR than the others.
– symplectomorphic
Jun 1 '14 at 14:57