Question

Give reasons.

1) Arithmetic mean is measure of central tendency.

2) Mode is that value which has maximum frequency.

3) Mode has a number of merits.

4) Median divides the series into two equal parts.

5) Mean has not any limitations.

6) Median is not affected by remote values.

7) Percentiles divide the data into hundred equal parts.

Answer 1

1. The central value represents the entire data in the sense that the values of observations in the data lie close to the central value. Arithmetic mean is the average of all items in the series. It is based on all the items in the data. Thus, it can be interpreted as a value that is an indicative of the various items in the data. Hence, we can say that arithmetic mean is a measure of the central tendency.

2. The mode is the observation or value that repeats itself the maximum number of times in the given series. Here, the frequency represents the number of times the value is repeated. Thus, it is correct to say that the mode is the observation or value that has the maximum frequency.

Example: The following marks are scored by 10 students in a class. Find the modal marks.

Student (Roll No.)	Marks Scored
1	15
2	17
3	14
4	15
5	15
6	15
7	18
8	14
9	12
10	13

A close examination of the data reveals that 15 occurs the highest number of times in the series i.e. 4 times. Thus, 15 is the modal marks.

3. Any observation that repeats itself the maximum number of times is called the mode of that data. The following are some of the merits of mode:
i. It is one of the simplest measures of central tendency and can be calculated by the mere inspection of the series.
ii. It can be presented graphically.
iii. It is not affected by the extreme values of the series.
iv. Calculation of mode does not require all the details about the series. It can be calculated for open-ended classes as well.

4. The median is the middlemost value of a set of data when it is arranged in an array (ascending or descending). Half of the items lie after the median and half of the items lie before the median; thus, the median divides the entire series into two equal parts.

5. The mean has both merits and demerits. The following are a few limitations of the mean:
i. It is largely affected by the extreme values of the series.
ii. Because it is based on all observations of the series, it cannot be calculated for open-ended classes.
iii. Sometimes, it gives absurd results, which are impractical.

6. The median is the middlemost value of a set of data when it is arranged in an array (ascending or descending). It is just a positional average that is based on the number of observations in the series and not on the values of those observations. In other words, it is the number of observations and not the values of the observations that affect the median. Thus, we can say that the median does not get affected by the remote values.

7. A percentile divides the given set of data into 100 equal parts. There are a total of 99 percentiles that divide the data into 100 parts, giving 99 dividing points. Each group contains an equal number of observations, thus giving 100 groups of equal size. Thus, we can say that percentiles break data into 100 equal parts.