Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
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 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.
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?