Solve the given inequality for real \(x:\frac{ (2x -1)}{3} ≥ \frac{(3x -2)}{4} - \frac{(2-x)}{5}\).
Solve the given inequality for real\(x: \frac{x}{4} < \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}\).
Solve the given inequality for real\(x: \frac{1}{2}(\frac{3x}{5}+4) ≥ \frac{1}{3}(x-6)\).
Solve the given inequality for real \(x: \frac{3(x - 2)}{5} ≤ \frac{5(2 - x)}{3}\).
Solve the given inequality for real\(x:\frac{ x}{3} > \frac{x}{2} +1\).
The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
(i) If wrong item is omitted.
(ii) If it is replaced by 12.
Given that \(\bar{x}\) is the mean and \(σ2\) is the variance of n observations x1,x2,...,xn. Prove that the mean and variance of the observations ax1,ax2,ax3,...,axn are \(a\bar{x}\) and \(a^2σ2\), respectively,\((a ≠ 0).\)
The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
\(\sum_{i=1}^{50}x_i=212,\sum_{i=1}^{50}x_i^2=902.8,\sum_{i=1}^{50}y_i=261,\sum_{i=1}^{50}y_{i=1}^2=1457.6\)
Which is more varying, the length or weight?
The following is the record of goals scored by team A in a football session:
For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?