Question

State whether, the following statements are true or false and rewrite them.

1) Mode is the value having maximum frequency.

2) Median is not affected by extreme items.

3) Arithmetic mean is not based on all observations.

4) Mode can be calculated by mere inspection.

5) Mean is not rigidly defined.

6) First decile is greater than first quartile.

Answer 1

1. The given statement is true.
Explanation
Any observation that repeats itself the maximum number of times is the mode of that data. Thus, it would be correct to say that the mode is that observation or value that has the maximum frequency.

2. The statement is true.
Explanation
The median is the middlemost value of any set of data arranged in an array. It is just a positional average, thereby, is not affected by the presence extreme values.

3. The given statement is false.
Explanation
The arithmetic mean is the sum total of all observations divided by the total number of observations. It includes all the observations given in the series.

4. The given statement is absolutely true.
Explanation
The mode is the observation or value that repeats itself the maximum number of times or that has the maximum frequency. Thus, it can be easily inspected or located by merely looking at the given data.

5. The given statement is false.
Explanation
The mean is said to be rigidly defined because even if we use any method of calculation of mean, we will get the same result. In other words, the resultant value remains the same, irrespective of the method we use.

6. The given statement is false.
Explanation
Deciles divide data into 10 equal parts, whereas quartiles divide data into 4 equal parts. Therefore, the 1^st decile would mean 1/10^th of the data, whereas the 1^st quartile would imply 1/4^th of the data. Hence, we can say that the 1^st decile is smaller than the 1^st quartile.