Effect of adding a constant value to the observations on measures of central tendency and dispersion

When a constant value is added to all the observations in a data set, it affects the measures of central tendency and dispersion in different ways.

Effect on measures of central tendency:

Adding a constant value to all the observations in a data set does not change the shape of the distribution, but it shifts the distribution to the right or left. As a result, the measures of central tendency also change, but in a predictable way.

1. Mean: Adding a constant value to all the observations increases the sum of the observations by the same value, but the number of observations remains the same. Therefore, the mean of the data set also increases by the same value. For example, if the mean of a data set is 50 and we add 10 to all the observations, then the new mean would be 60.

2. Median: Adding a constant value to all the observations does not change the relative position of the observations in the data set. Therefore, the median of the data set also remains unchanged.

3. Mode: Adding a constant value to all the observations does not change the frequency distribution of the data set. Therefore, the mode of the data set also remains unchanged.

Effect on measures of dispersion:

Adding a constant value to all the observations in a data set also affects the measures of dispersion in different ways.

1. Range: Adding a constant value to all the observations increases the range of the data set by the same value. For example, if the range of a data set is 20 and we add 10 to all the observations, then the new range would be 30.

2. Variance and Standard Deviation: Adding a constant value to all the observations does not change the shape of the distribution, but it shifts the distribution to the right or left. Therefore, the variance and standard deviation also remain unchanged.

3. Mean Deviation and Quartile Deviation: Adding a constant value to all the observations increases the deviation of each observation from the mean by the same value. Therefore, the mean deviation and quartile deviation also increase by the same value.

Answer Explanation:

In this question, all the observations are increased by 10. Therefore, the measures of central tendency (mean, median, mode) would be increased by 10, but the measures of dispersion (range, variance, standard deviation) would remain unchanged. Since the mean deviation and quartile deviation depend on the deviation of each observation from the mean, they would also be increased by 10. Therefore, the correct answer is option 'D' - all these three remain unchanged.

All the divation i.e ( SD,QD,MD) are independent of origin(+/-).[change in origin doesnt affect the deviations].
as given in the que all are added by20.(+) which means it is a origin therefor SD, QD, MD remains the same.