Arithmetic Elementary Statistics Quiz-2

Solution:
let the number of data be n
so sum of data = mean \times number of data
= 5n
now 10 is subtracted to each data
so now sum becomes = 5n-10n =-5n
mean = sum of data /no. of data
=\frac{-5n}{n} = -5
so new mean becomes -5

Video solution:

Solution:
Find the mean
\frac{(8+9+12+15+16+20+24+30+32+34)}{10}
\frac{(200)}{10}
20
Find the distance of each value from that mean


Step 3:- Find the mean of those distances
\frac{(12+11+8+5+4+0+4+10+12+14)}{10}
\frac{80}{10}
=8

Video solution:

Solution:
Let us assume that the 10th number is x .
we know that,
\sigma = \left [ \sqrt{\frac{\sum (x_{i}-\mu )^{2}}{N}} \right ]
N = Number of terms.
Given that,
standard deviation = 2 .
Mean = 8 .
N = 10 .
sum of square of 9 numbers = 599.
10th number = x .
So,
sum of square of all 10 numbers = Sum of square of 9 numbers+10th Number^{2}
Putting all values now , we get :-
2=\sqrt{\frac{599+x^{2}}{10}}-(8^{2})
Squaring both sides,we get
4={\frac{599+x^{2}}{10}}-(8^{2})
4+64={\frac{599+x^{2}}{10}}
68\times 10=599+x^{2}
x^{2}=81
x=9

Video solution:

Solution:

Let’s sort the given data - 14, 18, 26, 32, 35, 38, 52, 65

mean = 35

median=\frac{32+35}{2}=33.5

Difference = 35 - 33.5 = 1.5

Value = 1.5 \times8 = 12

65-12 = 53

Solution:

Solution:
Mean=\frac{\text{sum of observations}}{\text{number of observations}}
x=\frac{5+7+10+14+x+25+32+19}{8}
112+x=8x
7x=112
x=16

Video solution:

Solution:
\sigma = \left [ \sqrt{\frac{\sum (x_{i} - \mu)^{2}}{N}} \right ]
\mu=\frac{average}{mean}
=21336
\sigma=\sqrt{\frac{1}{5}(2^{2}+1^{2}+0^{2}+1^{2}+2^{2})}
\sigma=\sqrt{\frac{1}{5}(4+1+1+4)}
\sigma=\sqrt{\frac{10}{5}}
\sigma=\sqrt{2}
=1.41

Video solution:

Solution:
For, 29 observations mean is 33
sum=33\times 29=957
and for 30 observations,mean is 34
sum=34\times 30=1020
Difference=1020-957
=63(30th number)

Video solution:

Solution:
The sequence is
15, 10, 17, 13, 25, 17, 11, 18, 14, 19, 12, 20

Mode=17
Range=25-10=15
Median=16
mean of these three=\frac{17+15+16}{3}
mean of these three=\frac{48}{3}
mean of these three=16

Solution:



 

 

\sum (f_{i})=37
\sum (f_{i})\times (u_{i})=1155
Mean=\frac{\sum (f_{i})\times (u_{i})}{\sum (f_{i})}
Mean=\frac{1155}{37}
Mean=31.21

Video solution: