Measures of Central Tendency and Dispersion
Find the mean of the following sample observations.
17,51,16,7,31,36,25,18,22,31
Mean=Σx/n =Sum of all observations/n
=17+51+16+7+31+36+25+18+22+31=254
254/10= 25.4
List all the outcomes when a fair die is rolled
{1}, {2},{3},{4},{5},{6}
Find the range of the data 24,10,6,80,15,21,34
6,10,15,21,24,34,80
Largest =8=
Smallest= 6
Range=80-6
=74
A day of the week is selected at random. Find the probability that it is Sunday
P(Sunday)=1/7
Find the median of the following observations
6,7,6,8,99,25,7,70,18
6,6,7,7,8,18,25,70,99
x ~= (n+1/2)th
=(9+1/2)th
=5th
The 5th observation is 8
List all possible outcomes when a couple plans to have 3 children
S= {BBB,BBG,BGB,BGG,GBB,GBG,GGB,GGG}
Find the mean of the data in the given table
X 0 1 2 3 4
f 6 2 4 8 5
X 0 1 2 3 4
f 6 2 4 8 5 Σf= 25
Xf 0 2 8 24 2 ΣXf=54
54/25=2.16
There are 23 Republicans and 13 Democrats. If a senator is randomly selected, what is the probability that he or she is Republican?
Let event E represent a Republican.
Then, P(E) = n(E)/n(S)
= 23/23+13
= 23/36
The amounts of contributions (in $) for the Christmas gift for the secretaries in an office are 20,70,10,60,30,20,40,60,60,10,60. Find the mean, median and mode.
Mean = 10+10+20+20+30+40+60+60+60+60+70=440/11
= 40
Median=
40
Mode=60
Construct the sample space for the experiment of rolling a fair die.
S={1,2,3,4,5,6}
Find the mean median and mode of the Group frequency distribution.
Grade F
40-49 3
50-59 5
60-69 6
70-79 9
80-89 8
90-100 7
Grade F Midpoint f*m Cf
40-49 3 44.5 133.5 3
50-59 5 54.5 272.5 8
60-69 6 64.5 387.5 14
70-79 9 74.5 670.5 23
80-89 8 84.5 676 31
90-100 7 95 665 38
=38 =2804.5
Mean= 2804.5/38= 73.8 ( The mean is in the 70-79 interval
Mode= 9 (70-79 interval)
Median= 1/2 of 38= 19 (in the range of 70-79)
A family consists of the parents, two grandparents,3 sons and 3 daughters. One of them should be chosen to make dinner. Find the probability that it will be one of the grandparents or a female.
P(G or F)=P(G)+P(F)-P(G and F)
P(G)= P(Grandparents are chosen)=2/10
P(F)=P(female is chosen)=5/10
P(G and F)=P(Grandmother is chosen)=1/10
P(G and F)=2/10+5/10-1/10=3/5
The average of 6 numbers is 48. When a seventh number is added, the average is 47. What is the seventh number.
Sum of 6 numbers= 48*6=288
Sum of 7 numbers= 47*7=329
=329-288
=41
A fair die is rolled 20 times, and the following outcomes are recorded. Use Empirical probability to find the probability of rolling a 2.
4,1,1,2,6,5,1,6,2,6
2,5,4,1,3,1,3,6,2,5
P(E)= f/n=4/20
=1/5=0.2
Find the standard deviation of the Grouped Data
Grade f
50-59 3
60-69 5
70-79 9
80-89 12
90-100 8
Grade f Midpoint f*m x̄ m- x̄ (m- x̄) 2 f(m- x̄)2
50-59 3 54.5 163.5 79.2 -24.7 610.09 1830.27
60-69 5 64.5 322.5 79.2 -14.7 216.09 1080.45
70-79 9 74.5 670.5 79.2 -4.7 22.09 198.81
80-89 12 84.5 1014 79.2 5.3 28.09 337.08
90-100 8 95 760 79.2 15.8 249.64 1997.12
=37 =2930.5 =5448.73
x̄ = Σf*m/f =2930.5/37 = 79.2
S=√ Σf(m-x̄)2 / n-1
= √5443.73/37-1 =√151.2147...
=12.3
Given the Sample Space of rolling die, list 5 different events and label them.
E1-{3}
E2- {1,3,5}
E3- {6,1,5}
E4-{2,4,5}
E5-{1,2,3,4,5,6}
The mean of 17, 22,20,x,25,23 is 20. Find the value of x
17+22+20+25+23=107
107+x/6=20/1
107+x=20*6
107+x=120
x=120-107=13
In a residential community, the probability of randomly selecting a lawyer is 60%. the probability of selecting a female is 40%. The probability of selecting a female lawyer is 30%. If a resident is randomly selected from this community, what is the probability that the resident will be a lawyer or a female?
P(L or F) =P(L) +P(F)-P(L and F )
0.6+0.4-0.3
=0.70
Compute the variance of the data 6,6,3,2,8,5,5
(Round up to 2 decimal places)
mean=6+6+3+2+8+5+5
=35/7=5
Subtract 5 from each number in the data and sqaure them
1,1,-2,-3,3,0,0,
When squared = 24
Variance= 24/7=3.43
A fair die is rolled 10 times. Find the probability that a 6 will show up exactly 5 times
10*9*8*7*6/5*4*3*2*1=252
=252*1/65 5/610-5
=252*3125/610
=252*3125/60466176
= 787500/60466176
0.013