MUNHUMUTAPA FACULTY OF COMMERCE
Weekend Class
GROUP ASSIGNMENT
STUDENT NAME STUDENT NUMBER
MUKUMBACHORE MOLEEN M215647
MUNGURE VICTORY M212631
DEGREE PROGRAMME : LOGISTICS & TRANSPORT MANAGEMENT
LEVEL : PART TWO SEMESTER ONE
COURSE TITLE : STATISTICS
COURSE CODE : HMM 122
LECTURER : MS GUMBO
LECTURER’S COMMENT:
…………………………………………………………………………………….
1
QUESTION 1
Variable categorical or discrete or measurement
numerical continuous scale
Name of Internet service Categorical Nominal
provider
Time in hours spent Numerical Continuous Interval
surfing the Internet per
week
Number of emails Numerical Discrete Ratio
received in a week
Number of online Numerical Discrete Ratio
purchases made in a
month
QUESTION 2
Variable Type of data Measurement
Monthly payments: Quantitative data Ratio
$1,927
Number of jobs in past 10 Quantitative data Ratio
years: 1
Annual family income: Quantitative data Ratio
$76,000
Marital status: Married Qualitative data Nominal
QUESTION 3
Describe the population of interest. full-time first-year students who have
completed their first semester is the
population of interest
Describe the sample that was collected All sampled ( Census)
Describe a parameter of interest. The population proportion
Describe the statistic used to estimate the Sample proportion
parameter in (c).
2
Bar chart of radiation
mistakes
Missed all or part of intended target Wrong dose given
Wrong patient treated Other
300 284
255
250
200
150
100
50
50 32
0
1
Pie chart of radiation mistakes
Other
Wrong patient
5%
treated
8%
Missed all or
Wrong dose part of in-
given tended target
41% 46%
Missed all or part of intended target Wrong dose given
Wrong patient treated Other
QUESTION 5
To construct a histogram chart, draw a horizontal axis (x-axis) to represent the categories and a
vertical axis (y-axis) scaled to show either the frequency counts or the percentages of each
category. Then construct vertical bars for each category to the height of its frequency count (or
3
percentage) on the y-axis. Note that the sum of the heights across the bars must equal the sample
size (or 100%). The bars must be of equal width to avoid distorting a category’s importance.
However, neither the order of the categories on the x-axis, nor the widths of the bars matter. It is
only the bar heights that convey the information of category importance. Instead of drawing
vertical bars as we do for a histogram chart, we could merely mark the position of the top end of
each bar and then join up these points with straight lines. When we do this, the result is a
frequency polygon.
QUESTION 6
The following set of data is from a sample of n=5:
7 4 9 8 2
Mean
Mean = 7+4+9+8+2
5
30/5
6
Median
2. 4. 7. 8. 9.
The median is 7 if the numbers are arranged in ascending order
Mode
The data has no mode
Range
Max value - Min Value
9 - 2
7
X ẍ (x -ẍ ) (x - ẍ)2
7 6 1 1
4
4 6 -2 4
9 6 3 9
8 6 2 4
2 6 -4 16
30 34
Σf(x -
ẍ)2
Variance = Σf(x - ẍ)2
N
34
5
6.80
Standard deviation = √ variance
√ 6.80
2.6076
Coefficient of Standard deviation *
variation = 100
Mean
2.6076 * 100
6
0.4346
43.46%
QUESTION 7
5
Compute the first quartile, the third quartile and the interquartile range.
Lower quartile
2. 4. 7. 8. 9.
Q1 position = ¼ (n + 1)
¼*6
= 1.5
Q1 = 2 + 0.5 ( 4 – 2 )
= 3
Upper quartile
Q3 position = ¾ * (n + 1)
3/4 * 6
= 4.5
Q3 = 8 + 0.5 ( 9 – 8 )
= 8.5
Interquartile range
Q3 - Q1 = 8.5 - 3
= 5.5
Covariance
X y ẍ ⱥ (x -ẍ ) (y - ⱥ ) (x -ẍ ) (y - ⱥ)
7 21 8.08 24.25 -1.08 -3.25 3.51
5 15 8.08 24.25 -3.08 -9.25 28.49
8 24 8.08 24.25 -0.08 -0.25 0.02
3 9 8.08 24.25 -5.08 -15.25 77.47
6 18 8.08 24.25 -2.08 -6.25 13
10 30 8.08 24.25 1.92 5.75 11.04
12 36 8.08 24.25 3.92 11.75 46.06
4 12 8.08 24.25 -4.08 -12.25 49.98
9 27 8.08 24.25 0.92 2.75 2.53
15 45 8.08 24.25 6.92 20.75 143.59
18 54 8.08 24.25 9.92 29.75 295.12
97 291 88.88 266.75 8.12 24.25 670.81
8.08 24.25
6
Covariance 670.81
X Y X2 ΣXY Y2
1 7 21 49 147 441
2 5 15 25 75 225
3 8 24 64 192 576
4 3 9 9 27 81
5 6 18 36 108 324
6 10 30 100 300 900
7 12 36 144 432 1296
8 4 12 16 48 144
9 9 27 81 243 729
10 15 45 225 675 2025
11 18 54 324 972 2916
97 291 1073 3219 9657
ΣX ΣY
ΣX2 ΣXY ΣY2
11* 3219 - 97*291
11*1073-97*97
35409 - 28227
2394 * 21546
7182
7182
1.0
The relationship is a perfect strong positive
7
QUESTION 8
B B" Total
A 10 30 40
A" 25 35 60
Total 35 65 100
Probabilit 10 /
y A/B 100 0.1
Probabilit A" / 35 /
y B" 100 0.35
Probabilit 30 /
y A / B" 100 0.3
Yes events A and B are independent
QUESTION 9
If P( A∧B)=0.4 and P(B)=0.8 , find P ( A|B ).
= 0.4
0.8
= 0.5
QUESTION 10
8
The probability that both cards are queens (Without replacement)
= 4/52 * 3/51
= 0.0045
The probability that the first card is a 10 and the second card is a 5 or 6
= 4/52 *8/51
= 0.0121
The probability that both cards are queens (with replacement)
= 4/52 * 4/52
= 0.0059
The probability of getting blackjack in this problem
= 12/52 *1/52
= 0.0044
QUESTION 11
Expected return
Economic Conditions Probability Asset X X
Recession 0.1 -50 -5
Slow Growth 0.3 20 6
Moderate Growth 0.4 100 40
Fast Growth 0.2 150 30
71
Expected return
Economic Conditions Probability Asset Y Y
Recession 0.1 -100 -10
Slow Growth 0.3 50 15
Moderate Growth 0.4 130 52
9
Fast Growth 0.2 200 40
97
Asset X
Economic Asset Expected (x -
Conditions Probability X return X (x -ẍ ) ẍ)2 P(x - ẍ)2
Recession 0.1 -50 -5 -121 14641 1464.1
Slow Growth 0.3 20 6 -51 2601 780.3
Moderate
Growth 0.4 100 40 29 841 336.4
Fast Growth 0.2 150 30 79 6241 1248.2
71 3829
Variance 3829
Standard deviation √ Variance
√ 3829
61.87
Asset Y
Economic Asset Expected (y -
Conditions Probability Y return X (y -ẍ ) ẍ)2 P(y - ẍ)2
Recession 0.1 -100 -10 -197 38809 3880.9
Slow Growth 0.3 50 15 -47 2209 662.7
Moderate
Growth 0.4 130 52 33 1089 435.6
Fast Growth 0.2 200 40 103 10609 2121.8
97 7101
Variance 7101
Standard deviation √ Variance
√ 7101
84.27
10
Covariance of X & Y
Economic
Conditions Probability (x -ẍ ) (y -ẍ ) (x -ẍ ) ( y - x) P (x -ẍ ) ( y - x)
Recession 0.1 -121 -197 23837 2383.7
Slow Growth 0.3 -51 -47 2397 719.1
Moderate
Growth 0.4 29 33 957 382.8
Fast Growth 0.2 79 103 8137 1627.4
5113
Covariance 5113
Asset Y is a better investment because of high expected return.
QUESTION 12
Probability five questions correct?
n
P(x) = Cx Px (1-P)n – x
5
P (x = 5) = C5 (1/4)5 * (3/4)0
= 0.00098
Probability of at least four questions correct?
P (x ≥ 4 ) = P ( x = 4 ) + P (x = 5)
5
P ( x = 4) = C4 (1/4)4 * (3/4)1
= 0.0146
P (x ≥ 4 ) = 0.00098 + 0.0146
= 0.01558
Probability of no questions correct?
5
P ( x = 0) = C0 (1/4)0 * (3/4)5
11
= 0.2373
Probability of no more than two questions correct
P(x≤2) = 1 - ( P (x =0) + P (x = 1) + P (x = 2) )
5
P(x=1) = C1 (1/4)1 * (3/4)4
= 0.3955
5
P(x=2) = C2 (1/4)2 * (3/4)3
= 0.2637
P ( x ≤ 2 ) = 1 - ( 0.2373 + 0.3955 + 0.2637)
= 1 - 0.8965
= 0.1035
QUESTION 13
The distribution follows a Poisson
U= 2
a. if λ=2.5 , find P ( X=2 )
P((x = 2) = e-2.5 * 2.52
2ᴉ
= 0.2565
12
b. if λ=8.0 , find P ( X=8 )
P((x = 8) = e-8 * 88
8ᴉ
= 0.1396
c. if λ=0.5 , find P ( X=1 )
P((x = 0.5) = e-0.5 * 0.51
1ᴉ
= 0.3033
d. if λ=3.7 , find P ( X=0 )
P((x = 0) = e-3.7 * 3.70
0ᴉ
= 0.0247
13
