Arithmetic Elementary Statistics Quiz-3

Solution:
mean of 26 observations is 29
Sum of 26 observations=26\times 29=754
When 4 more observations are added
Average of 30 observations=32
Sum of observations=30\times 32=960
Difference is 960-754=206(sum of 4 observations)
Mean of 4 observations=\frac{206}{4}
Mean of 4 observations=51.5

Solution:
Mode=Value for which corresponding frequency is the highest
In the given sequence 8 is most repeated frequency.
Mode=8

Solution:
Given Sequence=2,5,9,8,15,12,9,2,19,21,11
Median=\frac{9+11}{2} = 10
Mean=\frac{2+5+9+8+15+12+9+2+19+21+11}{2}
Mean=11.1
Difference=11.1-10=1.1

Solution:
Mode=3median-2 mean
Mode=12,Mean=9
12=3 median-2\times 9
3 median=12 + 18
median=\frac{30}{3}
median=10

Solution:
Total of 50 numbers 10 are threes,15 are fours,18 are fives and 7 are sixes.

Mean=\frac{10\times 3+15\times 4+18\times 5+7\times 6}{50}
Mean=4.4=a

Mode=5=b(value of most repeated frequency)
Median=\frac{50}{2}(25th,26th term average)
Median=\frac{4+5}{2}
Median=4.5=c
a+2b-c=4.44+2\times 5-4.5
=9.94

Solution:
Coefficient of variation is given by C_{v}=\frac{S_{D}}{Mean}\times 100
C_{v}=\frac{4}{10}\times 100
C_{v}=40%

Solution:
Employees salaries=50, 55, 60, 65, 70, 72, 75, 80, 84, 89.
\sigma = \left [ \sqrt{\frac{\sum (x_{i} - \mu)^{2}}{N}} \right ]
Mean(\mu)=\frac{50+55+60+65+70+72+75+80+84+89}{10}
Mean(\mu)=70
\sigma=\sqrt{\frac{1}{10}(20^{2}+15^{2}+10^{2}+5^{2}+0+2^{2}+5^{2}+10^{2}+14^{2}+19^{2})}
\sigma=\sqrt{\frac{1}{10}(400+225+100+25+0+4+25+100+196+361)}
\sigma=\sqrt{\frac{1436}{10}}
\sigma=\sqrt{143.6}
\sigma=11.983

The algebraic sum of the deviations of a set of n values from their mean is always zero.

It is the formula for Binomial Distribution that is asked here which is given by

P(X = x) = ⁿC_x p^x q^(n-x).