Homework Chapter 3
Members of group:
Bùi Tấn Lộc-18521002
Bùi Quang Anh-18520441
Nguyễn Văn Bảo-18520494
Lê Thịnh-18521437
1.
The mean is the sum of all values divided by the number of values:
10+20+12+17+16 75
X= 5
= =15
5
Sort the data values from smallest to largest:
10,12,16,17,20
Since the number of values is odd, the median is the middle
value of the sorted data set: MEDIAN =16
2.
The mean is average value of all the samples, in other words, it is equal to
sum of the sample values devided by the number of the values included.
10+20+21+17+16+12 96
X= 6
= =16
6
To compute median, first sort the values:
10,12,16,17,20,21
There is even number of values (6), so the median is equal to the average of
the two middle values in sorted data:
16+17 33
Median= 2
= =16.5
2
3. Sort the data values from smallest to largest:
15,20,25,25,27,28,30,34
n is the number of values in the data set:
n= 8
x
The xth percentile is the ( 100 ×n ¿ th value (rounded up to the nearest integer;
or average of this value and the next in the case of an integer) in the sorted
data set
x 20
20th percentile → 100 ×n= 100 × 8=1.6 ≈ 2 →20
x 25 20+ 25
25th percentitle → 100 × n= 100 × 8=2→ 2
=22.5
x 65
65th percentitle → 100 × n= 100 × 8=5.2≈ 6 → 28
x 75 28+30
75th percentile → 100 × n= 100 × 8=6 → 2
=29
4. The mean is the sum of all values divided by the number of values:
53+ 55+70+…+69+ 57+68 657
X¿ = ≈ 59.7273
11 11
Sort the data values from smallest to largest:
53,53,53,55,57,58,64,68,69,70
Since the number of values is odd, the median is the middle value of the
sorted data set:
MEDIAN= 57
The mode is the most occurring value in the data set:
MODE= 53
5/88
a) The mean is the average of all data value:
nj 1 x j
MEAN = n
n=20 is the number of values in the data.
n
x j
j 1
= 163 + 177 + 166 + 126 + 123 + 120 + 144 + 173 + 160 + 192 + 125 + 167 + 245
+ 146 + 139 + 134 + 167 + 162 + 145 + 207 = 3,181
Therefore,
nj 1 x j 3,181
MEAN = n = 20 = 159,05
b) Sort the data values from smallest to largest: 120, 123, 125, 126, 134, 139, 144, 145,
146, 160, 162, 163, 166, 167, 167, 173, 177, 192, 207, 245.
Because n = 20 is even, the median is the average of the two middle values.
x( n /2) x(20/2) 160
x(( n 2)/2) x(22/2) 162
Therefore,
x(n/2) x(( x 2)/2) 160 162
161
MEDIAN = 2 = 2
c) The mode is the most occurring value in the data set:
Number 167 is repeated twice. Therefore, MODE = 167.
d) The first quartile is the median of the data values below the median (or at 25% of the
data):
The first quartile is going to be the median of these numbers: 120, 123, 125, 126, 134,
139, 144, 145, 146, 160. Here is n=10. Because n=10 is even, the median is the average
of the two middle values.
x( n /2) x(10/2) 134
x(( n 2)/2) x(12/2) 139
Therefore,
x( x /2) x(( x 2)/2) 134 139
Q1 136.5
2 2
e) The third quartile is the median of the data values above the median (or at 75% of the
data):
The third quartile is going to be the median of these numbers: 162, 163, 166, 167, 167,
173, 177, 192, 207, 245. Here is n = 10. Because n=10 is even, the median is the average
of the two middle values
x( n /2) x(10/ 2) 167
.
x(( n 2)/2) x(12/ 2) 173
Therefore,
x( n /2) x(( n 2)/2) 167 173
Q3 170
2 2
6/89
a) The mean is the sum of all values divided by the number of values:
Marketing Majors:
34.2 45 39.5 28.4 37.7 35.8 30.6 35.2 34.2 42.4
xM 36.3
10
Accounting Majors:
35.5 57.1 49.7 40.2 44.2 45.2 47.8 38 53.9 41.1 41.7 40.8 55.5 43.5 49.1 49.9
xA 45.7
16
Since the number of values is even, the median is the average of the middle values of the
sorted data set:
Marketing Majors:
35.2 35.8
MEDIAN M 35.5
2
Accounting Majors:
44.2 45.2
MEDIAN A 44.7
2
The mode is the most occurrung value in the data set:
Marketing Majors:
MODEM 34.2
Accounting Majors:
MODE A = Does not exist
b)
Marketing Majors:
The first quartile is the median of the data values below the median (or at 25% of the
data):
The first quartile is going to be the median of these numbers: 28.4, 30.6, 34.2, 34.2, 35.2.
Here is n = 5.
x( n /2) x(5/ 2) 34.2
x(( n 2)/2) x(7/2) 34.2
Therefore,
x x 34.2 34.2
Q1 ( n / 2) (( n 2)/2) 34.2
2 2
The third quartile is the median of the data values above the median (or at 75% of the
data):
Q3 39.5
Accounting Majors:
The first quartile is the median of the data values below the median (or at 25% of the
data):
Q1 40.95
The third quartile is the median of the data values above the median (or at 75% of the
data):
Q3 49.8
c) The starting salaries for accounting majors are higher than the marketing majors,
because all measures are higher for the accounting majors.
7/89
a) The mean is the sum of all values divided by the number of values:
n
x j
j 1
=
30+24.99+54+17+55+12.95+49.95+35+25+40+39+9.95+50+45+24+35+17+39.95+55+4
5+50+48+29.95+40
= 871.74
Therefore,
n
x
j 1
j
871.74
x= n = 24 =36.3225
Since the number of values is even, the median is the average of the middle values of the
sorted data set:
39 39.95
MEDIAN = 2 =39.475
The mode is the most occurring value in the data set:
MODE = 17, 35, 40, 45, 50, 55
b) The mean is the sum of ll values divided by the bumber of values:
29.95 10.99 24.95 5 29.95 9.95 14.95 19.75 15 20 62.5 10.55 29.95 14.95 14 12.95 7
x
24
19.95 24.95 17.95 19.95 20 19.95 36
20.4642
Since the number of values is even, the median is the average of the middle values of the
sorted data set:
19.75 19.95
MEDIAN 19.85
2
The mode is the most occurring value in the data set:
MODE = 29.95
c) 100 shares at $50 per share is more expensive, because the mean and median are
higher in part (a) compared to part (b).
d) The cost of the transaction is related to the amount of the transaction, because the cost
will be less for a smaller transaction.
8).
a. The mean is x=(18+20+25…+48+53+54)/20=34.75
The mode is 25(3 times).
b. After sorting in descending order we have the median is average of two middle values:
MEDIAN=(33+36)/2=34.5
c. For Q1
i=(p/100)*n=(25/100)*20=5. Because i=5 so the first quarticles is the average value of the 5th and 6th
values: (25+26)/2= 25.5
for Q3
i=(p/100)*n=(75/100)*20=15. Because i=15 so the third quarticles is the average value of the 14th and
15th values: (42+45)/2=43.5
d. i=32/100*20=6.4. Because i=6.4 not is an integer, so the 32th percentile is the data value 7 th position or
27.
9).
a)The mean number of minutes of usage per month:
X=(105+135+180+….+690+830+1180)/15=422
b)After sorting in descending order we have the median is the 8 th value or 380
c)The 85th percentile is:
i=(85/100)*20=12.75. Because i=12.75 is not an integer, so the 85 th percentile is 13th or 690
d) we have 13/15 user in the data set are under the reported upperlimit
so we have the percentage user under the reported about: 13/15*100=87%.
10)
a) The mean ER Waiting Times for Hospital at Full Capacity:
x=(47+50+50+…93+110+115)/14=76
The medium is the average value of two middle values 7 th anh 8th : (73+79)/2=76
b) The mean ER Waiting Times for Hospital at Balance:
x=(18+26+29…+54+56+60)/12=39
The median is the average value of two middle values 6 th anh 7th :(38+39)/2=38.5
c. The ER Waiting Times is too big.
Exercise 11/ 91
X(city) =( 16.2 + 16.7 + 15.9 + 14.4 + 13.2 + 15.3 + 16.8 + 16.0 + 16.1 + 15.3 + 15.2 + 15.3 + 16.2 ) / 13
= 15,586
X(Highway) = ( 19.4 + 20.6 + 18.3 + 18.6 + 19.2 + 17.4 + 17.2 + 18.6 + 19.0 + 21.1 + 19.4 + 18.5 +
18.7 ) / 16
= 18,9231
Median(city) = 15,9
Median(highway) 18,7
Mode(city) = 15,3
Mode(highway) =18,6
City driving requires less miles per gallon than highwat driving , because all
measures of center are higher for highway driving
Exercise 12 / 91
Total:
Disney = 346 + 325 + 253 + 304 + 448 + 354 + 169 + 273 + 110 + 136 + 250 + 104 + 249 = 3321
Pixar = 362 + 363 + 485 + 525 + 865 + 631 = 3231
Disney Movies have a slightly higher revenue than Pixar Movies
The Mean :
X( Disney ) = 3321 / 13 = 255,5
X( Pixar ) = 3231 / 6 = 538,5
The Pixar Movies have higher average revenue per movie made than Disney
Movies
Median:
Q(Disney) = (1/2) x 13 = 6,5 =7 => Median(Disney) = 253
Q(Pixar) = (1/2) x 6 = 3 => Median(Pixar) = ( 485 + 525) / 2 = 505
First quartile
Median of first 25
Q(Disney) = 0,25 x 13 = 3,25 = 4 => Q( Disney ) =169
Q(Pixar) = 0,25 x 6 =1,5 = 2 => Q( Pixar ) = 363
Third quartile :
Median of first 25
Q(Disney) = 0,75 x 13 = 9,75 =10 => Q(Disney) = 325
Q(Pixar) = 0,75 x 6 = 4,5 =5 => Q(Pixar) = 631
