STA1610/201/1/2020
Tutorial letter 201/1/2020
Introduction to Statistics
STA1610
Semester 1
Department of Statistics
SOLUTIONS TO ASSIGNMENT 01
Define tomorrow.
university
of south africa
QUESTION 1
Option (5)
A statistic is summary measure calculated from a sample to describe characteristics of a population.
QUESTION 2
Option (2)
A statistic is a property of a sample while a parameter is a property of a population.
QUESTION 3
Let us use variables from Table 1.1 as an illustrative example to help us answer option 2, 3 and 4.
1. Correct
2. Correct
Using dominant form of impairment as an example we can determine the frequency of each
element i.e. social interaction has a frequency of 108, communication has a frequency of 44
and etc.
3. Correct
We can determine the mode for qualitative data.
Using dormant form of impairment, as and example; “Repetitive behavior” is the mode since
it is the most frequent of the five attributes i.e. repetitive behavior has a high frequency of
206.
4. Incorrect
We cannot calculate the mean of forminant form of impairment.
5. Incorrect
QUESTION 4
Option (4)
The mean age of diagnosis calculated from a sample is a statistic.
QUESTION 5
Option (5)
In this example age is measured on a continuous scale i.e. age at diagnosis takes the form of
decimals.
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QUESTION 6
Option (2)
Tip: A quantitative discrete variable comes from a counting process. Whenever a variable is the
number of something, then that particular variable has to be quantitative discrete.
QUESTION 7
A. Incorrect
Type of ASD is measured on a nominal scale.
B. Correct
C. Correct
D. Correct
Option (3)
QUESTION 8
Option (2)
QUESTION 9
A. Correct
B. Correct
C. Incorrect
Frequency refers to count per class while relative frequency refers to the proportion of items
in a class.
D. Correct
Option (3)
QUESTION 10
Option (1)
3
EXTRA PRACTICE (USING TABLE 1.1A)
Add a column of relative frequency to table 1.1a and calculate the relative frequency for each type
of ASD and confirm the relative frequencies sum up to 1.
Type ASD
A
B
C
D
E
Total
Number of people
108
44
206
85
57
???
Relative frequency
?
?
?
?
?
1
QUESTION 11
Option (1)
QUESTION 12
Option (3)
QUESTION 13
1. Correct
2. Incorrect
The frequency of people living with type B ASD is 44.
3. Correct
The relative frequency of people living with type C ASD is
4. Correct
Option (2)
QUESTION 14
Option (1)
QUESTION 15
Option (4)
QUESTION 16
Option (4)
4
206
= 0.412.
500
STA1610/201/1/2020
QUESTION 17
Option (5)
QUESTION 18
Median: First order the data
44
57
Position of median
)
Mean
85 108 206
|{z}
Median
n+1
5+1
=
=3
2
2
Median = 85
P
xi
n
44 + 57 + 85 + 108 + 206
=
5
=
Mean =
500
= 100
5
1. Incorrect
2. Incorrect
3. Incorrect
4. Correct
Option (3)
QUESTION 19
S=
s
(xi − x̄)2
n−1
) First calculate x̄. From question 18 we know that the mean is equal to 100.
xi
108
44
206
85
57
500
xi − x̄
8
−56
106
−15
−15
0
(xi − x̄)2
64
3136
11236
225
225
16510
Total
5
r
16510
p 4
=
4127.500
= 64.25
S =
Option (1)
QUESTION 20
S
× 100%
x̄
64.25
=
× 100%
100
= 64.25%
CV =
Option (1)
QUESTION 21
1. Incorrect
2.
Q 1 (position)
n+1
4
6
=
4
= 1.5
=
Since the decimal is exactly · 5. Q 1 (value) is calculated by taking the average between the
1st and
2nd observation.
)
44 + 57
2
= 50.5
Q 1 (value) =
3.
Q 2 (position)
6
n+1
2
6
=
2
= 3
=
STA1610/201/1/2020
4.
Q 3 (position)
n+1
×3
4
6
=
×3
4
= 45
=
Since the decimal is exactly · 5, Q 3 (value) is calculated by taking the average between the
4th and 5th observation.
)
108 + 206
2
= 157
Q 3 (value) =
5. Incorrect
A distribution is symmetric if values of the mean, median and mode are equal.
Option (4)
QUESTION 22
I Q R = Q3 − Q1
= 157 − 50.5
106.5
Since the range is the maximum value subtract, the minimum value, IQR will always be less than
the range.
Option (2)
QUESTION 23
From the given information events A and B are mutually exclusive since an individual either lives
with ASD or does not live with ASD i.e. both events can’t occur at the same time.
Option (4)
QUESTION 24
P (A or B) = P (A) + P (B) − P (A and B)
If two events are mutually exclusive than P (A and B) = 0.
)
P (A or B) = 0.96 + 0.04 − 0 = 1
Option (3)
7
To answer questions 25 to 30 first complete table i.e.
Boy
Speech Therapist (ST )
90
Neuropsychologist (N P) 45
Psychiatrist (P)
30
Total
165
Girl
30
15
10
55
Total
120
60
40
220
QUESTION 25
P (N P and Boy) =
45
= 0.205
220
Option (5)
QUESTION 26
P (N P or Boy) = P (N P) + P (Boy) − P (N P and Boy)
60
165
45
=
+
−
220 220 220
60 + 165 − 45
=
220
180
=
220
= 0.818
Option (2)
QUESTION 27
P (Boy and N P)
P (N P)
45
= 220
60
220
45
=
60
= 0.75
P (Boy|N P) =
Option (3)
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QUESTION 28
1. Correct; P (Boy) =
165
= 0.75
220
(
)
(
)
(
) 165
55
220
2. Correct; P Boy or Girl = P (Boy) + P Girl − P Boy and Girl =
+
−0=
=1
220 220
220
3.
(
)
(
)
(
)
P Girl or ST = P Girl + P (ST ) − P Girl and ST
55
120
30
=
+
−
220 220 220
55 + 120 − 30
=
220
145
=
220
= 0.659
4.
P (ST ) =
120
= 0.545
220
5.
P (ST or N P) = P (ST ) + P (N P) − P (ST and N P)
120
60
=
+
−0
220 220
180
=
220
= 0.818
Option (3)
QUESTION 29
1.
P (ST and Boy) =
2.
90
= 0.409
220
(
)
10
P P and Girl =
= 0.045
220
9
3.
P (ST and Boy)
P (Boy)
90
= 220
165
220
90
=
165
= 0.545
P (ST |Boy) =
4.
(
(
)
P N P and Girl
(
)
P Girl
15
= 220
55
220
15
=
55
= 0.273
)
P N P|Girl =
5.
P (N P|Boy) =
=
=
=
P (N P) =
)
=
P (N P|Boy) =
Option (4)
P (N P and Boy)
P (Boy)
45
220
165
200
45
165
0.273
60
220
0.273
(
)
P N P|Girl = P (N P)
QUESTION 30
1. If events N P and Boy are independent then;
P (N P and Boy) = P (N P) × P (Boy)
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OR
P (N P|Boy) = P (N P) i.e. N P is independent of Boy.
Use either one of the two criteria to check for independence.
Using the first criteria
45
220
= 0.205
60
165
P (N P) × P (Boy) =
×
220 220
= 0.205
P (N P and Boy) =
) Events N P and Boy are independent.
2. Using the 2nd criteria we know from question 29, option (5) that
(
)
P N P|Girl = P (N P)
) Event N P and Girl are independent.
3. Events psychiatrist and boy are independent if
P (P|Boy) = P (P)
30
P (P|Boy) =
= 0.182
165
40
P (P) =
= 0.182
220
) Event Psychiatrist and Boy are independent.
4. Correct
(
)
P (Boy) = 0.75 is greater than P Girl = 0.25.
5. Correct
In this question there is no specialist who is a speech therapist and also a psychiatrist.
Option (3)
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