In a perfectly symmetric distribution which of the following

In a perfectly symmetric distribution, which of the following statements is false? The distance from the smallest observation to Q2 is the same as the distance from Q2 to the largest observation The distance from Q1 to Q2 equals to the distance from Q2 to Q3 The distance from Q1 to Q3 is half of the distance from the smallest to the largest observation The distance from the smallest observation to Q1 is the same as the distance from Q3 to the largest observation

Solution

It is false that the distance from Q1 to Q3 is half of the distance from the smallest to the largest observation .

Because the distance between Q1 and Q3 measures that which gives the range covered by middle half of the data.