Question

Child height (cm)	Father height (cm)	Gender
145.0	136.5	M
125.5	121.0	M
125.5	119.5	M
133.5	128.0	M
126.0	135.5	M
142.5	131.0	M
127.5	134.5	M
133.5	132.5	M
130.5	133.5	M
131.0	126.0	M
136.0	124.0	M
132.5	146.5	M
132.0	134.5	M
121.5	142.0	M
131.0	119.0	M
136.0	133.5	M
134.5	118.5	M
138.5	134.0	F
128.5	132.0	F
140.5	131.5	F
134.5	141.5	F
132.5	136.5	F
126.0	136.5	F
143.0	136.0	F
130.0	143.0	F
123.5	134.0	F
143.5	146.0	F
140.0	137.0	F
132.5	136.5	F
138.5	144.0	F
135.0	139.0	F
135.0	136.0	F

using the Minitab software:

a. Construct an appropriate chart to represent the Genders

b. Construct a histogram (using 6 classes or groups) and a stem and leaf for the child height

c. Describe the shape of the distribution in question2.

d. Are there any unusual observations for the Father height?

e. Construct the Box plot and Stem-Leave for the child’s height.

Answer 1

a.

b.

Stem-and-Leaf Display: Child height (cm)

Stem-and-leaf of Child height (cm) N = 32
Leaf Unit = 1.0

1 12 1
2 12 3
4 12 55
7 12 667
8 12 8
12 13 0011
(6) 13 222233
14 13 4455
10 13 66
8 13 88
6 14 00
4 14 233
1 14 5

(c) From histogram and stem-leaf plot, the distribution is almost symmetric.

(d)

Stem-and-leaf of Father height (cm) N = 32
Leaf Unit = 1.0

3 11 899
4 12 1
4 12
5 12 4
6 12 6
7 12 8
9 13 11
13 13 2233
(5) 13 44445
14 13 6666667
7 13 9
6 14 1
5 14 23
3 14 4
2 14 66

Descriptive Statistics: Father height (cm)

Variable Q1 Median Q3 IQR
Father height (cm) 131.13 134.50 136.88 5.75

Lower whisker=Q1-1.5IQR=131.13-1.5*5.75=122.505

Upper whisker=Q3+1.5IQR=136.88+1.5*5.75=145.505

Any value which lies outside the interval (122.505, 145.505) is called outlier. Hence 118,119,119,121,146,146 are outliers or unusual observations.

e.