Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13.
2
4
10
11
Correct answer is A
\(\begin{array}{c|c} x & x - x & (x - x)^2\\ \hline 7 & -3 & 9\\8 & -2 & 4 \\9 & -1 & 1\\10 & 0 & 1\\11 & 1 & 1\\ 12 & 2 & 4\\13 & 3 & 9\\ \hline & & 28\end{array}\)
S.D = \(\sqrt{\frac{\sum(x - x)^2}{N}}\)
= \(\sqrt{\frac{\sum d^2}{N}}\)
= \(\sqrt{\frac{28}{7}}\)
= \(\sqrt{4}\)
= 2
\(\frac{2}{11}\)
\(\frac{5}{11}\)
\(\frac{6}{11}\)
\(\frac{8}{11}\)
Correct answer is A
Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Prime numbers has only two factors
itself and 1
The prime numbers among the group are 23, 29. Probability of choosing a prime number
= \(\frac{\text{Number of prime}}{\text{No. of total Possible Outcomes}}\)
= \(\frac{2}{11}\)
11.5
12.5
14.0
14.5
Correct answer is D
Median = L1 + (\(\frac{Ef}{fm}\)) - fo
\(\frac{\sum f}{2}\)
= \(\frac{20}{2}\)
= 10, L1 = 10.5, fo = 6, fm = 5
Median = 10.5 + \(\frac{(10 - 6)}{5}\)5
= 10.5 + 4
= 14.5
27
35
38
49
Correct answer is D
Average age of 110 students = 16
∴ Total age = 16 x 10 = 160 years
Age of teachers = x, total number of people now = 11
mean age = 19
Total age of new group = 19 x 11 = 209
Age of teachers = x = (209 - 160) = 49 yrs
13.2g
15.0g
16.8g
17.5g
Correct answer is C
Mode = a + \(\frac{(b - a)(F_m - F_b)}{2F_m - F_a - F_b}\)
= \(L_1 + \frac{\Delta_1 x^\text{c}}{\Delta_1 + \Delta_2}\)
= \(10 + \frac{(20 - 10)(27 - 10)}{2(27) - 10 - 19}\)
= 10 + \(\frac{170}{25}\)
= 10 + 6.8
= 16.8