Question

(17) IS IT POSSIBLE for each of the following descriptive statistical outcomes to occur ? Please   ALSO BRIEFLY EXPLAIN ANY FOUR RESPONSES !

(A) MEDIAN = 29, for a data set which ranges from 27 to 86.

(B) STANDARD DEVIATION = 3500, for a data set which ranges from 58 to 138.

(C) VARIANCE is negative.

      (D) Q₁ = Q_3.

(E) ∑ ( X - X BAR ) = - 3.2

(F) Q₂ > Q₃

(G) MODE = 159, for a data set which ranges from 84 to 157.5.

Answer 1

(A) Median = 29, for a data ranges from 27 to 86. Median is just the middlemost value in the dataset. So, Yes, it can be possible. For example, this dataset 27, 28, 29, 70, 86 has median 29.

(B)

i.e standard deviation is just the root mean square deviation. So, these is generally the square root term. But standard deviation of 3500 is quite very large and it is not possible within range 58 to 138.

(C) Variance = (Standard Deviation)²

Variance is a square term and it is not possible for a square term to be negative. So, this statement is not possible.

(D) First quartile and Third quartile can be equal when all the data in the dataset are equal. But, if all the data are unequal, then this cannot be possible.

(E) No, this is not possible because -

(F) For finding quartiles, we have to first arrange the data in ascending order. So, it is general to have Q₃ > Q₂ > Q₁. So this is false.

(G) Mode is the value in the dataset which occurs in highest frequency. For data range from 84 to 157.5 it is not possible to have mode 159.