Box plot
Edexcel S1 Mathematics 2003
(or box and whisker plot)
Introduction
Box plot diagrams:provide a diagrammatic representation
of the distribution use quartiles to divide the distribution
into intervals each containing ¼ of the data values
used to compare distributionsused to show skewness of distribution
Find the quartiles Use any given algorithm to calculate outliers find the values of the whiskers Draw a box plot to scale– on graph paper
Stages in drawing a box plot
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
(c) Comment on the skewness of these data.
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
(c) Comment on the skewness of these data.
This question uses a small number of datavalues for ease of calculations. The number of data values is usually larger. Very few data values can make the calculation of quartiles less meaningful.
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
(c) Comment on the skewness of these data.
Any rule to identify outliers will be specified inthe question. The rule provided here is a typicalone.
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
(c) Comment on the skewness of these data.
Make sure you use graph paper to draw a boxplot. Ask for graph paper in the moduleexam.
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
Possibly use a stem and leaf diagram tore-order the data
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
1 1 3 4 4 5 6 9 10 21
The median is the middle value:n/2 = 10/2 = 5 5.5th value =
Q2
Whole number - so
round up
to --.5th Find average of 5th and 6th value
2
54
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
1 1 3 4 4 5 6 9 10 21
The median is the middle value:n/2 = 10/2 = 5 5.5th value = = 4.5 mins
The lower quartile, Q1, is the 1/4th value:n/4 = 10/4 = 2.25 3rd value =
2
54
Q2
Not whole - so round
up
to whole
Find the 3rd value
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
1 1 3 4 4 5 6 9 10 21
The median is the middle value:n/2 = 10/2 = 5 5.5th value = = 4.5 mins
The lower quartile, Q1, is the 1/4th value:n/4 = 10/4 = 2.25 3 mins 3rd value =
2
54
Q1 Q2
Not whole - so round
up
to whole
Find the 3rd value
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
1 1 3 4 4 5 6 9 10 21
The median is the middle value:n/2 = 10/2 = 5 5.5th value = = 4.5 mins
The lower quartile, Q1, is the 1/4th value:n/4 = 10/4 = 2.25 3 mins
The upper quartile, Q3, is the 3/4th value:3n/4 = 3x10/4 = 7.75 8th value =
3rd value =
2
54
Q1 Q2
Not whole - so round
up
to whole
Find the 8th value
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
1 1 3 4 4 5 6 9 10 21
The median is the middle value:n/2 = 10/2 = 5 5.5th value = = 4.5 mins
The lower quartile, Q1, is the 1/4th value:n/4 = 10/4 = 2.25 3 mins
The upper quartile, Q3, is the 3/4th value:3n/4 = 3x10/4 = 7.75 8th value = 9 mins
3rd value =
2
54
Q1 Q3Q2
Not whole - so round
up
to whole
Find the 8th value
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
Answer re-order the data:
1 1 3 4 4 5 6 9 10 21
The median is the middle value:n/2 = 10/2 = 5 5.5th value = = 4.5 mins
The lower quartile, Q1, is the 1/4th value:n/4 = 10/4 = 2.25 3 mins
The upper quartile, Q3, is the 3/4th value:3n/4 = 3x10/4 = 7.75 8th value = 9 mins
The inter quartile range = Q3 – Q1 = 9 – 3 = 6 mins
3rd value =
2
54
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6Check below Q1 for outliers:
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1Check below Q1 for outliers:
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
Answer calculate outliers:
Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 =
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Check above Q3 for outliers:
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Check above Q3 for outliers:
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Q3
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 =
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
*
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
*
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
*
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Remember to use GRAPH
paper
Answer calculate outliers:
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(c) Comment on the skewness of these data.
1 1 3 4 4 5 6 9 10 21
Q1 Q3Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9, IQR = 6
Q1 – 1.5 x IQR =Check below Q1 for outliers:
3 – 1.5 x 6 = -6 This falls outside the data range, so there is no outlier below Q1. So left whisker is the least value 1.
Q3 + 1.5 x IQR =Check above Q3 for outliers:
9 + 1.5 x 6 = 18 This falls within the data range. So value 21 is an outlier. The right whisker is 18.
Draw scale and boxplot:0 5 10 15 20 25
*
1 1 3 4 4 5 6 9 10 21
Q1 Q3Q2
Q3 - Q2 = 9 – 4.5 = 4.5 Q2 -Q1 = 4.5 – 3 = 1.5
So Q3 – Q2 > Q2 – Q1 So distribution is right (positive) skewed
Answer (a) median = Q2 = 4.5, IQR = 6
(b) boxplot: 0 5 10 15 20 25
*
(c) Q3 – Q2 > Q2 – Q1 So distribution is right (positive) skewed
Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 21, 3, 5, 10, 1, 4
(a) Find the median and inter-quartile range
An outlier is an observation that falls either 1.5 x (inter-quartile range) above the upper quartile or 1.5 x (inter-quartile range) below the lower quartile
(b) Draw a boxplot diagram to represent these data, indicating any outliers
(c) Comment on the skewness of these data.