Statistics for Economics for Class 11 Chapter 5 Measures of Central Tendency
Presentation of Data
1. Arithmetic Mean – In statistics, the Arithmetic Mean (AM), also called an average, is the ratio of the sum of all observations to the total number of observations. The arithmetic mean can also inform or model concepts outside of statistics. In a physical sense, the arithmetic mean can be thought of as a centre of gravity. From the mean of a data set, one can think of the average distance the data points are from the mean as standard deviation. The square of standard deviation (i.e. variance) is analogous to the moment of inertia in the physical model.
Arithmetic mean represents a number that is obtained by dividing the sum of the elements of a set by the number of values in the set.
2. Geometric Mean – The Geometric Mean (GM) is the average value or mean, which signifies the central tendency of the set of numbers by finding the product of their values. Basically, one multiplies the numbers altogether and takes the nth root of the multiplied numbers, where n is the total number of data values. For example, for a given set of two numbers, such as 3 and 1, the geometric mean is equal to √(3×1) = √3 = 1.732.
In other words, the geometric mean is defined as the nth root of the product of n numbers. It is noted that the geometric mean is different from the arithmetic mean.
3. Harmonic Mean – The Harmonic Mean (HM) is defined as the reciprocal of the average of the reciprocals of the data values. It is based on all the observations, and it is rigidly defined. The harmonic mean gives less weightage to the large values and large weightage to the small values to balance the values correctly. In general, the harmonic mean is used when there is a necessity to give greater weight to the smaller items. It is applied in the case of times and average rates.
4. Quartiles – Quartiles divide the entire set into four equal parts. So, there are three quartiles, first, second, and third, represented by Q1, Q2, and Q3, respectively. Q2 is nothing but the median, since it indicates the position of the item in the list and, thus, is a positional average. To find quartiles of a group of data, one has to arrange the data in ascending order.
5. Percentile – A percentile is defined as the percentage of values found under specific values. Percentiles are mostly used in the ranking system. It is based on dividing up the normal distribution of the values. Percentile is represented as xth, where x is a number. For example, assume that a student has the 80th percentile on a test of 150. By this, one can understand the term percentile better and know that by scoring 150 in the exam, a student has beaten 80% of the remaining class in the exam.
We hope that the offered Statistics for Economics Index Terms for Class 11 with respect to Chapter 5: Measures of Central Tendency will help you.
Related Links:
- Class 11 Statistics for Economics Terms – Chapter 1: Introduction
- Class 11 Statistics for Economics Terms – Chapter 2: Collection of Data
- Class 11 Statistics for Economics Terms – Chapter 3: Organisation of Data
- Class 11 Statistics for Economics Terms – Chapter 4: Presentation of Data
- Class 11 Statistics for Economics Terms – Chapter 7: Correlation
- Class 11 Statistics for Economics Terms – Chapter 8: Index Numbers
- Class 11 Statistics for Economics Terms – Chapter 9: Use of Statistical Tools
