Download LESSON 3 1-Variable Statist ungrouped data

Statistics and the TI-83
Lesson # 3
One-Variable Descriptive measures for ungrouped data
To compute the descriptive measures for ungrouped data we can use
I. Formulas
II. The 2nd LIST  MATH menu
III. The STAT CALC 1 (1-Var Stats) menu
I.
Using Lists and formulas to compute descriptive measures
Exercise 1. Consider the sample Y= {3, -5, 8, 2, 9, 4, 6, 5, -3, 10, -4, 11, 14, 10, 7}. Compute the
mean and median of the sample. Use the formula: mean 
Y

{3, -5, 8, 2, 9, 4, 6, 5, -3, 10, -4, 11, 14, 10, 7} STO

2nd LIST  OPS 3

dim ( 2nd LIST Y ) STO  ALPHA N

2nd LIST  MATH 5

 ALPHA N STO  ALPHA M (mean) ENTER
ENTER
to compute the mean
N
ALPHA Y ENTER
answer: 15 (odd number)
sum( 2nd LIST Y ) ENTER
answer: 77
answer: the mean is 5.13333333333

2nd LIST  OPS 1 Sort A ( 2nd LIST Y ) ENTER (done)

2nd LIST Y((ALPHA N +1)  2)
STO  ALPHA D
ENTER
answer: the median is 6
Exercise 2 . Consider the sample given by the list L1= {1,-3, 5, 7, 13, 5, 7, 9, 12, -6}
Use the formula: mean 
L
1
N
to compute the mean of the values in
L1 and store the result as M.
 {1, -3, 5, 7, 13, 5, 7, 9, 12, -6} STO 2nd L1 ENTER

2ndLIST  MATH 5

 2nd LIST  OPS 3 dim ( 2nd L1 ) STO  ALPHA M (mean) ENTER answer: 5
sum( 2nd L1 ) ENTER
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answer: 50
Exercise 3. Use the formula s 
2
 (x  mean)
2
n 1
to compute the variance of the numbers in
L1. Complete the table below. Find the standard deviation of the values in L1.
X (L1) (X-M)
( X  M )2
1
-3
5
7
13
5
7
9
12
-6
-4
-8
0
2
8
0
2
4
7
-11
16
64
0
4
64
0
4
16
49
121
338

2nd LIST OPS 3 dim( 2nd L1 ) STO ALPHA N

2nd L1 ENTER (check values on the X column)

2nd L1 - ALPHA M ENTER (check values on the second column)

^2 (to square the differences) ENTER

2nd LIST  MATH 5 sum( 2nd ANS ) ENTER

 (N-1) ENTER

(2nd ANS) ENTER
ENTER answer: 10
(check values on the third column)
answer: 338
answer: var=37.5555555
answer: standard deviation is 6.12825877
Exercise 4. Use the computational formula s 
2
 (x
 x 
)
2
2
N 1
N
to compute the variance of
the numbers in L1.
 2nd LIST  MATH 5



sum(2nd L1^2) STO  ALPHA A
ENTER
answer: 588
2nd LIST  MATH 5 sum( 2nd L1) ^2 STO  ALPHA B
ENTER
answer: 2500
(ALPHA A – ALPHA B  N)  (N -1) ENTER answer: 37.5555555
(2nd ANS) ENTER
answer: standard deviation is 6.12825877
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Exercise5. Write the elements of L1 in ascending order, SortA or
descending order, SortD. Find the median.

2nd List  OPS 1 Sort A ( 2nd L1 ) ENTER (done)

2nd L1 ENTER

(L1(5)+L1(6))/2 STO D (median) ENTER
answer: {-6 -3 1 5
5
7
7
9 12
13}
answer: 6
II. Using the LIST MATH MENU
Use the LIST MATH sub-menu to check the results above
Exercise 6: for the values in L1 find the mean, median, variance and standard deviation. Use the
LIST MATH MENU

2nd LIST
 MATH 3
ENTER
answer: 5

2nd LIST
 MATH 4 median (2nd L1 ) ENTER
answer: 6

2nd LIST
 MATH 8 Variance(2nd L1 ) ENTER

2nd LIST  MATH 7
mean(2nd L1 )
stdDev(2nd L1 ) ENTER
answer: 37.55555555
answer: 6.12825877
Exercise 7: for the values in list Y (exercise 1) find the mean, median, variance and standard
deviation. Use the LIST MATH MENU

2nd LIST
 MATH 3

2nd LIST
 MATH 4 median (2nd LIST Y ) ENTER

2nd LIST
 MATH 8 Variance(2nd LIST Y) ENTER

2nd LIST  MATH 7
mean(2nd LIST Y)
ENTER
stdDev(2nd LIST Y) ENTER
Exercise 8. Find the mean and median of the numbers
answer: 5.13333333
answer: 6
answer: 32.55238095
answer: 5.705469389
2 3 1 3 5
, , , ,
3 5 8 8 6

2nd LIST  MATH 3

mean ({2  3, -3  5, 1  8, 3  8, 5  6} ) ENTER MATH 1

2nd LIST  MATH 4

median ({2  3, -3  5, 1  8, 3  8, 5  6} ) ENTER MATH 1
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ENTER
ENTER
answer: 7/25
answer: 3/8
Exercise 9. Find the standard deviation of the numbers
2 3 1 3 5
, , , ,
3 5 8 8 6

2nd LIST  MATH 7

stadDev ({2  3, -3  5, 1  8, 3  8, 5  6} ) ENTER
answer: 0.5619472593
III. Using the STAT CALC
Exercise 10. Use the STAT CAL C menu to find descriptive measures of the sample used in
exercise 1 given by list Y.

STAT
 CALC 1 1-Var Stats 2nd LIST Y
ENTER ENTER
x  5.133333333 (mean)
 x  77 sum of the values
 x  851 sum of the squares 
2
Sx  5.705469389 sample s tan dard deviation
x  5.512007096  population s tan dard deviation
n  15
min X  5
Q1  2 ( first quartile )
Q3  10 third quartile 
Med  6 (media )
MaxX  14 (max imum)
Exercise 11. Use the STAT CAL C menu to find descriptive measures of the sample used in
exercise 1 given by list L1

STAT
 CALC 1 1-Var Stats 2nd L1
ENTER
x  5 (mean)
 x  50 sum of the values
 x  588 sum of the squares 
2
Sx  6.12825877 sample s tan dard deviation
x  5.813776741  population s tan dard deviation
n  10
min X  6
Q1  1 ( first quartile )
Q3  9 third quartile 
Med  6 (media)
MaxX  13 (max imum)
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Exercise 12: compute the standard deviation of the following sample: -3, 5, 7, 9,12, 6, 15.
a) Use the formula given below
 x 
2
x
Use the formula: s 
2

n 1
n

{-3, 5, 7, 9, 12, 6, 15} STO  X ENTER

2nd LIST X^2

2nd LIST OPS 3 ENTER dim(2nd LIST X)

2nd LIST MATH 5 sum (2nd LIST X2) STO  S ENTER answer: S=569

2nd List MATH 5

STO  X2
2nd LIST

stdDev({-3, 5, 7, 9, 12, 6, 15})
 MATH
2nd LIST

stdDev(2nd LIST X)
STAT
answer: T= 51
answer: s= 5.736267245
7
MATH

 MATH
3) Using STAT
ENTER answer: 7
MATH

c) Using 2ndLIST
STO N
sum(2nd List X) STO  T ENTER
((S -T^2/N)/(N-1)) ENTER
b) Using 2nd LIST

ENTER
CALC
 CALC
7
ENTER
Ans.: 5.736267245
LX
7
ENTER
1-Var Stats
Ans.: 5.736267245
ENTER
1 1-Var Stats 2nd LIST X ENTER ENTER
answers: see the given descriptive statistical report, s=5.736267245, etc.
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