Advanced Programming Techniques (2011, 2013)

Appendix B. Answers to Desk Checks

117

Chapter 1. Arrays

Desk Check 1.1 Fill
list				x	i
8.3	8.3	8.3	8.3	8.3	0
[0]	[1]	[2]	[3]		1
					2
					3
					4

Desk Check 1.2 Ramp
list					i
0	1	2	3	4	0
[0]	[1]	[2]	[3]	[4]	1
					2
					3
					4
					5

Desk Check 1.3 Reverse Ramp
list					high	i
4	3	2	1	0	4	0
[0]	[1]	[2]	[3]	[4]		1
						2
						3
						4
						5

Desk Check 1.4 Reverse
list					left	right	swap
~~3.4~~ 12	−2 7	5 5	7 −2	~~−12~~ 3.4	0	4	3.4
~~3.4~~ 12	−2 7	5 5	7 −2	~~−12~~ 3.4	1	3	−2
[0]	[1]	[2]	[3]	[4]	2	2

Desk Check 1.5 Rotate Left
list					i	swap	last
9 23	23 18	18 −3	−3 8	8 9	0	9	4
9 23	23 18	18 −3	−3 8	8 9	1
[0]	[1]	[2]	[3]	[4]	2
					3
					4

118

Desk Check 1.6 Rotate Right
list					i	last	swap
9 8	23 9	18 23	−3 18	8 −3	4	4	8
9 8	23 9	18 23	−3 18	8 −3	3
[0]	[1]	[2]	[3]	[4]	2
					1
					0

Desk Check 1.7 Rotate
list						group	one	two	save
11 −3	23 14	−5 11	9 23	−3 −5	14 9	0	0	4	11
11 −3	23 14	−5 11	9 23	−3 −5	14 9		4	2
[0]	[1]	[2]	[3]	[4]	[5]		2	0
						1	1	5	23
k	n	groups					5	3
2	6	2					3	1
4						2

Desk Check 1.8 gcd
a	b	r	return
2	6		2
2	6	2
6	2	0

Desk Check 1.9 printRotated
list						index	i	console output
11	23	−5	9	−3	14	−2		[−3,14,11,23,−5,9]
[0]	[1]	[2]	[3]	[4]	[5]	4
						5	0
k	n	separator				6	1
2	6	""				0	2
		", "				1	3
						2	4
						3	5
						4	6

Desk Check 1.10 Linear Search
list					key	i	return
28.1	20	23.6	0	15	23.6	0	2
[0]	[1]	[2]	[3]	[4]		1
						2

119

Desk Check 1.11 Binary Search
list
−2.1	−1	3.9	6.2	7.1	9.7	10	12	13.1	15.6	18	19	20.1	24.5
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]	[11]	[12]	[13]

key	left	right	mid	cmp	return
15.6	0	13	6	5.6	9
	7		10	−2.4
		9	8	2.5
	9		9	0

Desk Check 1.12 Find a Range
purchase	rate	discount	return
$708.00	0.025	17.7	690.3

Desk Check 1.13 Find a Range
purchase	rate	discount	return
$708.00	0.025	17.7	690.3

Desk Check 1.14 Find a Range
limits			rates
300	600	1000	0	0.02	0.025	0.03
[0]	[1]	[2]	[0]	[1]	[2]	[3]

purchase	i	rate	discount	return
$708.00	0	0.025	17.7	690.3
	1
	2

Desk Check 1.17 Arabic to Roman
arabic	exponent	divisor	digit	roman
1987				""
987	3	1000	1	"M"
87	2	100	9	"MCM"
7	1	10	8	"MCMLXXX"
0	0	1	7	"MCMLXXXVII"

Desk Check 1.18 Roman to Arabic
roman	exponent	length	chars	digit	arabic
"MCMLXXXVII"					0
	3	4	"MCML"	−1
		3	"MCM"	−1
		2	"MC"	−1
		1	"M"	1	1000
"CMLXXXVII"	2	4	"CMLX"	−1
		3	"CML"	−1
		2	"CM"	9	1900
"LXXXVII"	1	4	"LXXX"	8	1980
"VII"	0	4	"VII"	7	1987

120

Desk Check 1.20 Sort by Name or Age
students			console output
"Jane" 18	"Sam" 17	"Nigel" 14	[Jane 18, Sam 17, Nigel 14]
[0]	[1]	[2]	[Jane 18, Nigel 14, Sam 17]
			[Nigel 14, Sam 17, Jane 18]

Desk Check 1.21 Insertion Sort
list					first	last	i	swap	j
6	−8	9	7	0	0	4	3	7	4
6	−8	9	0	7					5
							2	9	3
6	−8	0	7	9					4
									5
							1	−8	2
6	−8	0	7	9
							0	6	1
−8	0	6	7	9					2
[0]	[1]	[2]	[3]	[4]					3
							−1

Desk Check 1.22 findCandidates
candidates
"cash"	"charity"	"clothing"	"dentist"	"dividend"	"doctor"	"education"
[0]	[1]	[2]	[3]	[4]	[5]	[6]

prefix	index	first	last	bounds
"c"	1	1	1	null
		0	2	0, 2
		−1	3
		0	2

Desk Check 1.23 findAnyCandidate
candidates
"cash"	"charity"	"clothing"	"dentist"	"dividend"	"doctor"	"education"
[0]	[1]	[2]	[3]	[4]	[5]	[6]

prefix	left	mid	right	term	cmp	return
"c"	0	3	6	"dentist"	−1	1
		1	2	"charity"	0

Desk Check 1.24 startsWithCompare
prefix	term	preLen	minLen	i	diff	return
"c"	"charity"	1	1	0	0	0
				1

121

Desk Check 1.25 findBestCandidate
candidates
"cash" 17	"charity" 8	"clothing" 6	"dentist" 7	"dividend" 14	"doctor" 11	"education" 4
[0]	[1]	[2]	[3]	[4]	[5]	[6]

prefix	index	max	save	i	freq	return
"d"	3	7	3	2		4
				3
	4	10		4	14
				5	11
				6

Desk Check 1.26 findAnyCandidate
candidates
"cash" 17	"charity" 8	"clothing" 6	"dentist" 7	"dividend" 14	"doctor" 11	"education" 4
[0]	[1]	[2]	[3]	[4]	[5]	[6]

prefix	left	mid	right	term	cmp	return
"d"	0	3	6	"dentist"	0	3

Chapter 2. Array Lists

Desk Check 2.1 append
this.array				this.count	c
'U'	'n'	'd'		2	'd'
[0]	[1]	[2]	[3]	3

Desk Check 2.2 append
this.array								this.count	i
'U'	'n'	'd'	'a'	'u'	'n'			3	0
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	4	1
								5	2
a								6	3
'a'	'u'	'n'
[0]	[1]	[2]

Desk Check 2.3 append
this.array								this.count	i
'U'	'n'	'd'	'a'	'u'	'n'			3	0
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	4	1
								5	2
sb.array					sb.count			6	3
'a'	'u'	'n'			3
[0]	[1]	[2]	[3]

122

Desk Check 2.4 append
this.array												this.count
'U'	'n'	'd'	'a'	'u'	'n'	't'	'e'	'd'				6
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]	[11]	9

newLen	s
9	"ted"

Desk Check 2.5 expandCapacity
old				this.count	suggest	capacity
'U'	'n'	'd'		3	6	8
[0]	[1]	[2]	[3]

this.array
'U'	'n'	'd'
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

Desk Check 2.6 findFibonacci
value	index	return
6	−2	8
	1

Chapter 4. Iteration and Recursion

Desk Check 4.1 Iterative n factorial
n	fact
4	4
3	12
2	24
1

Desk Check 4.2 Recursive n factorial
Function	Variables
factorial	n	return
	4	24
factorial	n	return
	3	6
factorial	n	return
	2	2
factorial	n	return
	1	1

123

Desk Check 4.4 Iterative GCD
x	y	r
472	24	16
24	16	8
16	8	0
8	0

Desk Check 4.5 Recursive GCD
Function	Variables
gcd	x	y	rem	return
	472	24	16	8
gcd	x	y	rem	return
	24	16	8	8
gcd	x	y	rem	return
	16	8	0	8

Desk Check 4.8 Recursive Sum
Function	Variables
sum	a				return
	6.5	7.1	6.9		20.5
	[0]	[1]	[2]
sumR				i	return
				0	20.5
sumR				i	return
				1	14.0
sumR				i	return
				2	6.9
sumR				i	return
				3	0

Desk Check 4.9 Tail Recursive Sum
Function	Variables
sum	a					return
	6.5	7.1	6.9			20.5
	[0]	[1]	[2]
sumR				s	i	return
				0	0	20.5
sumR				s	i	return
				6.5	1	20.5
sumR				s	i	return
				13.6	2	20.5
sumR				s	i	return
				20.5	3	20.5

124

Desk Check 4.11 Tail Recursive n Factorial
Function	Variables
factorial		n	return
		4	24
factorialR	f	n	return
	1	4	24
factorialR	f	n	return
	4	3	24
factorialR	f	n	return
	12	2	24
factorialR	f	n	return
	24	1	24

Desk Check 4.12 Recursive Pre-Order Traversal of a Binary Tree
Function	Variables
maxLen	return
	7
maxLenR	curr	max	len
	Simon	0 5 7	5
maxLenR	curr	max	len							curr	max	len
	John	5 7	4							Thomas	7	6
maxLenR	curr	max	len	curr	max	len				curr	max	len	curr	max	len
	null	5		Phillip	5 7	7				null	7		null	7
maxLenR				curr	max	len	curr	max	len
				null	7		null	7

Desk Check 4.13 Iterative Pre-Order Traversal
stack			curr	len	max
					0
Simon
			Simon	5	5
Thomas	John
			John	4
Thomas	Phillip	null
			null
			Phillip	7	7
Thomas	null	null
			null
			null
			Thhomas	6
null	null
[0]	[1]	[2]	null
			null

125

Desk Check 4.14 Recursive In-Order Traversal
Function	Variables
toList	list
	John	Phillip	Simon	Thomas
toListR	curr
	Simon
toListR	curr			curr
	John			Thomas
toListR	curr	curr		curr	curr
	null	Phillip		null	null
toListR		curr	curr
		null	null

Desk Check 4.15 Iterative In-Order Traversal
list
John	Phillip	Simon	Thomas
stack				frame
Simon, CheckLeft				node	todo
				Simon	CheckLeft
Simon, Process		John, CheckLeft
				John	CheckLeft
Simon, Process		John, Process
				John	Process
Simon, Process		Phillip, CheckLeft
				Phillip	CheckLeft
Simon, Process		Phillip, Process
				Phillip	Process
Simon, Process
				Simon	Process
Thomas, CheckLeft
				Thomas	CheckLeft
Thomas, Process
				Thomas	Process

Desk Check 4.16 Recursive Fibonacci Function
Function	Variables
fibonacci	n	return
	4	3
fibonacci	n	return			n	return
	2	1			3	2
fibonacci	n	return	n	return	n	return	n	return
	0	0	1	1	1	1	2	1
fibonacci							n	return	n	return
							0	0	1	1

126

Desk Check 4.17 Iterative Fibonacci Function
stack				frame	n	fib
				−1	4	0
4				0
				−1	4
3	2			1
				0	2
3	1	0		2
				1	0
				0	1	1
				−1	3
2	1			1
				0	1	2
				−1	2
1	0			1
[0]	[1]	[2]	[3]	0	0
				−1	1	3

Desk Check 4.18 Iterative Fibonacci Function
future	past	present	n
	0	1	4
1	1	1	3
2	1	2	2
3	2	3	1
5	3	5	0

Desk Check 4.19 Tail Recursive Fibonacci Function
Function	Variables
fibonacci	n	return
	4	3
fibonacciR	past	present	n	return
	0	1	4	3
fibonacciR	past	present	n	return
	1	1	3	3
fibonacciR	past	present	n	return
	1	2	2	3
fibonacciR	past	present	n	return
	2	3	1	3
fibonacciR	past	present	n	return
	3	5	0	3

127

Desk Check 4.20 Fibonacci Formula
SQRT5	GOLDEN	n	numer	return
2.236	1.618	4	6.708	3

Desk Check 4.23 Iterative Binary Search
list
−2.1	−1	3.9	6.2	7.1	9.7	10	12	13.1	15.6	18	19	20.1	24.5
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]	[11]	[12]	[13]

key	left	right	mid	cmp	return
15.6	0	13	6	5.6	9
	7		10	−2.4
		9	8	2.5
	9		9	0

Desk Check 4.24 Recursive Binary Search
list
−2.1	−1	3.9	6.2	7.1	9.7	10	12	13.1	15.6	18	19	20.1	24.5
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]	[11]	[12]	[13]

Function	Variables
binarySearch	key	return
	15.6	9
binarySearchR	key	left	right	mid	cmp	return
	15.6	0	13	6	5.6	9
binarySearchR	key	left	right	mid	cmp	return
	15.6	7	13	10	−2.4	9
binarySearchR	key	left	right	mid	cmp	return
	15.6	7	9	8	2.5	9
binarySearchR	key	left	right	mid	cmp	return
	15.6	9	9	9	0	9

Desk Check 4.25 Future Value
principal	annualRate	years	periodsPerYear	rate	periods	fv
10000	0.06	2	4	0.005	8	11265

Desk Check 4.26 Iterative Future Value
i	principal	annualRate	years	periodsPerYear	rate	periods
	10000	0.06	2	4	0.005	8
1	10150
2	10302
3	10457
4	10614
5	10773
6	10935
7	11099
8	11265
9

128

Desk Check 4.27 Recursive Future Value
Function	Variables
futureValue	principal	annualRate	years	periodsPerYear	rate	periods	return
	10000	0.06	2	4	0.005	8	11265
futureValueR	principal	rate	period	return
	~~10000~~ 10150	0.005	8 7	11265
futureValueR	principal	rate	period	return
	~~10150~~ 10302	0.005	7 6	11265
futureValueR	principal	rate	period	return
	~~10302~~ 10457	0.005	6 5	11265
futureValueR	principal	rate	period	return
	~~10457~~ 10614	0.005	5 4	11265
futureValueR	principal	rate	period	return
	~~10614~~ 10773	0.005	4 3	11265
futureValueR	principal	rate	period	return
	~~10773~~ 10935	0.005	3 2	11265
futureValueR	principal	rate	period	return
	~~10935~~ 11099	0.005	2 1	11265
futureValueR	principal	rate	period	return
	~~11099~~ 11265	0.005	1 0	11265
futureValueR	principal	rate	period	return
	11265	0.005	0 −1	11265

Chapter 5. Counting Bits

129

Desk Check 5.14 Naive
word	word & 1	n	i
		0	0
0011 0101	1	1	1
0001 1010	0		2
0000 1101	1	2	3
0000 0110	0		4
0000 0011	1	3	5
0000 0001	1	4	6
0000 0000	0		7
0000 0000	0		8

130

Desk Check 5.15 Loop Termination
word	word & 1	n
		0
0011 0101	1	1
0001 1010	0
0000 1101	1	2
0000 0110	0
0000 0011	1	3
0000 0001	1	4
0000 0000

Desk Check 5.16 Addition
word	word & 1	n
		0
0011 0101	1	1
0001 1010	0	1
0000 1101	1	2
0000 0110	0	2
0000 0011	1	3
0000 0001	1	4
0000 0000

Desk Check 5.17 Skip Zero Bits
word	n	word − 1
	0
0011 0101	1	0011 0100
0011 0100	2	0011 0011
0011 0000	3	0010 1111
0010 0000	4	0001 1111
0000 0000

Desk Check 5.18 Combinatorial
word	word >>> 1	ones	word >>> 1 & ones	word & ones
0011 0101	0001 1010	0101 0101	0001 0000	0001 0101

	word >>> 2	twos	word >>> 2 & twos	word & twos
0010 0101	0000 1001	0011 0011	0000 0001	0010 0001

	word >>> 4		(word >>> 4) + word	fours
0010 0010	0000 0010		0010 0100	0000 1111

0000 0100

Desk Check 5.19 Lookup
word	(int)word & 0xff	onbits[(int)word & 0xff]
0011 0101	0011 0101	4

131

Chapter 6. Sets

Desk Check 6.1 Contains
array
"apple"	"pear"	"plum"	"cherry"	"peach"
[0]	[1]	[2]	[3]	[4]

term	i	return
"plum"	0	true
	1
	2

Desk Check 6.2 Is Subset
					i	termA	return
this	"elm"	"pine"	"rose"		0	"elm"	false
	[0]	[1]	[2]		1	"pine"
					2	"rose"
setB	"lilac"	"pine"	"fir"	"elm"	3
	[0]	[1]	[2]	[3]

Desk Check 6.3 Intersection
					ceil	i	termA	n
this	"elm"	"pine"	"rose"	"lilac"	3			0
	[0]	[1]	[2]	[3]		0	"elm"
setB	"lilac"	"pine"	"fir"			1	"pine"	1
	[0]	[1]	[2]			2	"rose"
arrayC	"pine"	"lilac"				3	"lilac"	2
	[0]	[1]	[2]			4

Desk Check 6.4 Relative Complement
					ceil	i	termA	n
this	"elm"	"pine"	"rose"	"lilac"	4			0
	[0]	[1]	[2]	[3]		0	"elm"	1
setB	"lilac"	"pine"	"fir"			1	"pine"
	[0]	[1]	[2]			2	"rose"	2
arrayC	"elm"	"rose"				3	"lilac"
	[0]	[1]	[2]	[3]		4

132

Desk Check 6.5 Union
								ceil	i	termB	n
this	"elm"	"pine"	"rose"	"lilac"				7	0
	[0]	[1]	[2]	[3]					1
									2
setB	"lilac"	"pine"	"fir"						3
	[0]	[1]	[2]						4		4
									0	"lilac"
arrayC	"elm"	"pine"	"rose"	"lilac"	"fir"				1	"pine"
	[0]	[1]	[2]	[3]	[4]	[5]	[6]		2	"fir"	5
									3

Desk Check 6.6 Is Subset
					sizeA	sizeB	a	b	cmp	return
this	"elm"	"pine"	"rose"		3	4	0	0	0	false
	[0]	[1]	[2]				1	1	10
								2	4
setB	"elm"	"fir"	"lilac"	"pine"				3	0
	[0]	[1]	[2]	[3]			2	4

Desk Check 6.7 Intersection
					a	termA	b	termB	cmp	n
this	"elm"	"lilac"	"pine"	"rose"						0
	[0]	[1]	[2]	[3]	0	"elm"	0	"fir"	−1
					1	"lilac"			6
setB	"fir"	"lilac"	"pine"				1	"lilac"	0	1
	[0]	[1]	[2]		2	"pine"	2	"pine"	0	2
					3		3
arrayC	"lilac"	"pine"						sizeA	sizeB	ceil
	[0]	[1]	[2]					4	3	3

Desk Check 6.8 Relative Complement
					a	termA	b	termB	cmp	n
this	"elm"	"lilac"	"pine"	"rose"						0
	[0]	[1]	[2]	[3]	0	"elm"	0	"fir"	−1	1
					1	"lilac"			6
setB	"fir"	"lilac"	"pine"				1	"lilac"	0
	[0]	[1]	[2]		2	"pine"	2	"pine"	0
					3	"rose"	3			2
arrayC	"elm"	"rose"			4
	[0]	[1]	[2]	[3]				sizeA	sizeB	ceil
								4	3	4

133

Desk Check 6.9 Union
					a	termA	b	termB	cmp	n
this	"elm"	"lilac"	"pine"	"rose"						0
	[0]	[1]	[2]	[3]	0	"elm"	0	"fir"	−1	1
setB	"fir"	"lilac"	"pine"		1	"lilac"			6	2
	[0]	[1]	[2]				1	"lilac"	0	3
					2	"pine"	2	"pine"	0	4
	sizeA	sizeB	ceil		3	"rose"	3			5
	4	3	7		4

arrayC	"elm"	"fir"	"lilac"	"pine"	"rose"
	[0]	[1]	[2]	[3]	[4]	[5]	[6]

Desk Check 6.10 Add
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

bitset	term	index	found	i	return
0101 0000	"fir"	null	false	4	true
0101 1000

Desk Check 6.11 Remove
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"	"ash"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

bitset	term	index	i	found	return
1101 1000	"pine"	1	1	false	true
1001 1000				true

Desk Check 6.12 Contains
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"	"ash"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

bitset	term	index	found
1101 1000	"lilac"	3	true

134

Desk Check 6.13 Is Subset
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"	"ash"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

this.bitset	setB.bitset	temp	return
1110 000	1101 1000	1110 0000	false
		1100 0000

Desk Check 6.14 Intersection
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"	"ash"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

this.bitset	setB.bitset	result.bitset
1110 0000	1101 1000	1110 0000
		1100 0000

Desk Check 6.15 Relative Complement
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"	"ash"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

this.bitset	setB.bitset	result.bitset
1110 0000	1101 1000	1110 0000
		0010 0000

Desk Check 6.16 Union
universe.list
"elm"	"pine"	"rose"	"lilac"	"fir"	"ash"
[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]

this.bitset	setB.bitset	result.bitset
1110 0000	1101 1000	1110 0000
		1111 1000

135

Chapter 7. Statistics

Desk Check 7.1 Minimum
data				i	min
9	12.3	−3	5		9
[0]	[1]	[2]	[3]	1
				2	−3
				3
				4

Desk Check 7.2 Sum
data				i	s
7	3	−2	4.4		0
[0]	[1]	[2]	[3]	0	7
				1	10
				2	8
				3	12.4
				4

Desk Check 7.3 Sum
data				x	s
7	3	−2	4.4		0
[0]	[1]	[2]	[3]	7	7
				3	10
				−2	8
				4.4	12.4

Desk Check 7.4 Mean
data				s	return
7	3	−2	4.4	12.4	3.1
[0]	[1]	[2]	[3]

Desk Check 7.5 Two Pass Variance
data				m	i	x	t	sqsum	var
7	3	−2	4.4	3.1				0	10.73
[0]	[1]	[2]	[3]		0	7	3.9	15.21
					1	3	−0.1	15.22
					2	−2	−5.1	41.23
					3	4.4	1.3	42.92
					4

136

Desk Check 7.6 One Pass Variance
data				i	x	sum	sqsum	n	mean	var
7	3	−2	4.4			0	0	4	3.1	10.73
[0]	[1]	[2]	[3]	0	7	7	49
				1	3	10	58
				2	−2	8	62
				3	4.4	12.4	81.36

Desk Check 7.7 One Pass Correlation
dataX				i	x	y	sumX	sumY	sumX2	sumY2	sumXY
12	4	3.9	2.1				0	0	0	0	0
[0]	[1]	[2]	[3]	0	12	12	12	12	144	144	144
				1	4	3.2	16	15.2	160	154.24	156.8
dataY				2	3.9	3.5	19.9	18.7	175.21	166.49	170.45
12	3.2	3.5	1.9	3	2.1	1.9	22	20.6	179.62	170.1	174.44
[0]	[1]	[2]	[3]	4

n	meanX	meanY	sdevX	sdevY	covar	correl
4	5.5	5.15	3.83	4.00	15.29	0.998

Desk Check 7.8 Stable Mean
data				i	delta	mean
−2	3	4.4	7			−2
[0]	[1]	[2]	[3]	1	5	0.5
				2	3.9	1.8
				3	5.2	3.1

Desk Check 7.9 Stable Variance
data				i	weight	delta	mean	sqsum	var
−2	3	4.4	7				−2	0	10.73
[0]	[1]	[2]	[3]	1	0.5	5	0.5	12.5
				2	0.67	3.9	1.8	22.64
				3	0.75	5.2	3.1	42.92
				4

Desk Check 7.11 Multiple Statistics
data				i	x	weight	delta	mean	sqsum
−2	3	4.4	7					−2	0
[0]	[1]	[2]	[3]	1	3	0.5	5	0.5	12.5
				2	4.4	0.67	3.9	1.8	22.64
				3	7	0.75	5.2	3.1	42.92
				4

count	min	med	max	sum	var	sdev
4	−2	3.7	7	12.4	10.73	3.28

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