Download Practice problems 4 answers- 1

Statistics and the TI-84
Practice Problems 4: answers
One-Variable Descriptive measures for grouped data
Exercise 1. Consider the following distribution of X, with frequencies F.
X
2
5
1
10
3
8
F
4
7
3
5
4
6
a) Use the TI-83 calculator to re-arrange the table in ascending values of X

{2, 5, 1, 10, 3, 8} STO  X

{4, 7, 3, 5, 4, 6} STO  ALPHA F

2nd LIST OPS  1 SortA(2nd LIST X, 2nd LIST

2nd LIST X
ENTER
answer: {1 2 3 5 8 10}

2nd LIST F
ENTER
answer: {3 4 4 7 6 5}
ENTER
ENTER
F)
ENTER
Done
X
1
2
3
5
8
10
F
3
4
4
7
6
5
b) Find the descriptive measures of the variable X with frequency distribution shown in the table
above.
 STAT  CALC 1 1-Var Stats 2nd LIST X , 2nd LIST F ENTER
x  5.379310345 (mean of the distributi on)
 x  156
( sum of the x  values)
x
2
 1114 sum of the squared values of x 
S x  3.13293327 sample s tan dard deviation
 x  3.078443327 ( population s tan dard deviation
n  29 sample size  min X  1 (min imum value of X )
Q1  2.5 ( first quartile )
Median  5
Q3  8 (third quartile )
MaxX  10 (max imum value of X )
Exercise 2. Use the 2nd LIST MATH menu to find the standard deviation of the grouped data in
exercise 1.

2nd LIST  MATH 7 stdDev(2nd LIST X, 2nd LIST F) ENTER
-41-
answer: 3.13293327
Exercise 3. Use the B0X-and-WHISKER plot for exercise 1.

Y= (deselect all existing plots and functions, if necessary

2nd STAT PLOT
ON
ENTER

type BOX- PLOT ENTER X list: X
ENTER

WINDOW Xmin=-2

GRAPH
1
TRACE
Select
Xmax=15
minX=1
Ymin= 1
Q1=2.5
Freq:
F ENTER
Ymax=10
Med=5
Q3=8
maxX=10
Exercise 4. Use the STAT CALC menu to estimate the descriptive measures of the group data
given below
Class
4.2 – 7.6
7.7-11.1
11.2-14.6
14.7-18.1
18.2-21.6
F
17
6
12
8
5

Y= (deselect Plot1, Plot2)

{4.2, 7.7, 11.2, 14.7, 18.2} STO  ALPHA L

{ 7.6, 11.1, 14.6, 18.1, 21.6} STO  ALPHA U

{17, 6, 12, 8, 5}

(2nd LIST L +2nd LIST U)  2

STAT  CALC 1

1-Var Stats 2nd LIST X, 2nd LIST F ENTER
STO  ALPHA F
ENTER
ENTER
STO  X
ENTER
 x  542.2
x  11.29583333 (mean)
x
2
 7250.78
x  4.843335556
Sx  4.894589211
n  48
ENTER
min X  5.9
Q1  5.9
Median  12.9
Q3  16.4
MaxX  19.9
Exercise 5. Use the B0X-and-WHISKER plot for exercise 4.

Y= (deselect all existing plots and functions, if necessary

2nd STAT PLOT
ON
ENTER

type BOX- PLOT ENTER X list: X
ENTER

WINDOW Xmin=-2

GRAPH
TRACE
1
Select
Xmax=20
minX=5.9
Ymin= 1
Q1=5.9
-42-
Freq:
F ENTER
Ymax=20
Med=12.9
Q3=16.4
maxX=19.9

EXERCISE 6
Consider the following distribution of values
13
23
51
20
53
31
11
15
19
25
50
10
21
16
10
52
53
22
15
10
17
30
27
28
18
53
35
43
15
33
23
45
42
55
38
25
20
18
40
32
43
16
40
35
32
34
52
21
a) Construct the frequency table for the data using the classes
CLASSES 10-18
19-27
28-36
37-45
{13,
11,
21,
15,
18,
23,
15,
16,
10,
53,
51,
19,
10,
17,
35,
20,
25,
52,
30,
43,
53,
50,
53,
27,
15,
31,
10,
22
28,
33,
23,
45,
42,
55,
38,
25,
20,
18,
40,
32}
43,
16,
40,
35,

STO

2nd LIST

2nd L1

{15, 13, 13, 11, 8} STO ALPHA F6 ENTER
2nd L1
36
44
32
20
42
14
41
11
30
26
43
30
42,
14,
41,
11,
30,
26,
43,
30,
46-55
32,
34,
52,
21,
36,
44,
32,
20,
ENTER
 OPS
1
SortA( LL1) (sort ascending) ENTER
ENTER (from the sorted list determine the frequency of each class
CLASSES 10-18
19-27
28-36
37-45
46-55
F6
15
13
13
11
8
b) Use the STAT CALC menu to compute the descriptive measures of the group data given above.

{10, 19, 28, 37, 46 STO  ALPHA L

{ 18, 27, 36, 45, 55} STO  ALPHA U

(LL+LU)  2 STO  ALPHA ALPHA X6

STAT  CALC 1

1-Var Stats 2nd LIST X6, 2nd LIST F6 ENTER
x  31.86666667 (mean)
Sx  16.77514977
n  60
min X  14
ENTER
ENTER
ENTER
 x  1912
x
2
 77532
x  16.63476948
Q1  18.5
Median  32
Q3  41
MaxX  67
Exercise 7. Use 2nd LIST MATH to estimate the standard deviation by using the ungrouped data and the grouped
data.

2nd LIST  MATH 7 stadDev(2nd L1)

2nd LIST  MATH 7 stadDev(2nd LIST X6, 2nd LIST F6)
ENTER
-43-
answer: 13.3790776
ENTER
answer: 16.77514977