All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ?

Question :

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ?

(a) Mean

(b) Median

(c) Mode

(d) Variance

Solution :

If initially all marks were given \(x_i\), then

\({\sigma_i}^2\) = \(\sum(x_i – \bar{x})^2\over N\)

Now, each is increased by 10.

\(\therefore\) \({\sigma_i}^2\) = \(\sum((x_i + 10) – (\bar{x} + 10))^2\over N\)

= \({\sigma_i}^2\)

So, variance will not change whereas mean, median and mode will increase by 10.


Similar Questions

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is

The mean and the variance of a binomial distribution are 4 and 2, respectively. Then, the probability of 2 success is

In a series of 2n observations, half of them equals a and remaining half equal -a. If the standard deviation of the observation is 2, then |a| equal to

A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 g and a standard deviation of 2 g. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 g. The correct mean and standard deviation in gram of fishes are respectively.

Leave a Comment

Your email address will not be published.