Box and whiskers plots

2. BOX AND-WHISKERS PLOTS
Example-1.
From the data 6, 9, 12, 14, 8, 11
(a) Find all Quartiles
(b) Find minimum value and maximum value
(c) Draw Box and-Whiskers plots
(d) Comments on the shapes of distribution
Solution:
6, 8, 9 , 11, 12, 14
(a)
Q1 (Median of First half) = 8
Q2 (Median) = 10
2
119
=
+
Q3 (Median of 2nd
Half) = 12
(b) Minimum Value = 6
Maximum Value = 14
(c)
(d) Distribution is Symmetrical because Q3 – Q2 = Q2 – Q1
6 8 9 10 11 12 14

3. Example-2.
From the data 6, 8, 24, 20, 15, 18, 19, 13, 11
(a) Find all Quartiles
(b) Find minimum value and maximum value
(c) Draw Box and-Whiskers plots
(d) Comments on the shapes of distribution
Solution:
6, 8, 11, 13, 15, 18, 19, 20, 24
(a)
Q1 (Median of First Half) = 5.9
2
118
=
+
Q2 (Median) = 15
Q3 (Median of 2nd
Half) = 5.19
2
2019
=
+
(b) Minimum Value = 6
Maximum Value = 24
(c)
(d) Distribution is Negatively Skewed because
Q3 – Q2 < Q2 – Q1
6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 24

4. NOTE: Distribution is said to be Positively Skewed if
Q3 – Q2 > Q2 – Q1