Question 3:
Solution:
(a)
Mean ˉx=b1+a+2a+8+9+156=b33+3a=6b3a=6b−33a=2b−11 ------(1)New median =4b7(2a−3)+(8−3)2=4b72a+22=4b714a+14=8b7a=4b−7 ------(2)Substitute (1) into (2),7(2b−11)=4b−714b−77=4b−710b=70b=7From (1), a=2(7)−11=3
(b)
Variance, σ2=∑x2N−ˉx2σ2=(−2)2+(0)2+(3)2+(5)2+(6)2+(12)26−(−2+0+3+5+6+126)2σ2=2186−16=20.333
The mean of the data 1, a, 2a, 8, 9 and 15 which has been arranged in ascending order is b. If each number of the data is subtracted by 3, the new median is
47b
. Find
(a) The values of a and b,
(b) The variance of the new data.
Solution:
(a)
Mean ˉx=b1+a+2a+8+9+156=b33+3a=6b3a=6b−33a=2b−11 ------(1)New median =4b7(2a−3)+(8−3)2=4b72a+22=4b714a+14=8b7a=4b−7 ------(2)Substitute (1) into (2),7(2b−11)=4b−714b−77=4b−710b=70b=7From (1), a=2(7)−11=3
(b)
New data is (1 – 3), (3 – 3), (6 – 3), (8 – 3), (9 – 3), (15 – 3)
New data is – 2, 0, 3, 5, 6, 12
Question 4:
(b) A sum of certain numbers is 72 with mean of 9 and the sum of the squares of these numbers of 800, is taken out from the set of 20 numbers. Calculate the mean and variance of the remaining numbers.
Solution:
(a)
Mean ˉx=∑xN8=∑x20∑x=160Standard deviation, σ=√∑x2N−ˉx23=√∑x2N−ˉx29=∑x220−82∑x220=73∑x2=1460
(b)
Sum of certain numbers, M is 72 with mean of 9,72M=9M=8Mean of the remaining numbers=160−7220−8=713Variance of the remaining numbers=1460−80012−(713)2=55−5379=129
A set of data consists of 20 numbers. The mean of the numbers is 8 and the standard deviation is 3.
(a) Calculate
∑x
and
∑x2
.
(b) A sum of certain numbers is 72 with mean of 9 and the sum of the squares of these numbers of 800, is taken out from the set of 20 numbers. Calculate the mean and variance of the remaining numbers.
Solution:
(a)
Mean ˉx=∑xN8=∑x20∑x=160Standard deviation, σ=√∑x2N−ˉx23=√∑x2N−ˉx29=∑x220−82∑x220=73∑x2=1460
(b)
Sum of certain numbers, M is 72 with mean of 9,72M=9M=8Mean of the remaining numbers=160−7220−8=713Variance of the remaining numbers=1460−80012−(713)2=55−5379=129