Harmonic Mean (HM) is defined as the reciprocal of the arithmetic average of the reciprocal of the value of various items. It can be solved through the following formula: In Case of Individual Series: Example 1: Calculate the HM from the following data: X: 18 12 16 21 7 9 Solution: Calculation of HM: HM = N/∑(1/x)= 6/1.0358 [...]
This article throws light upon the four main forms of frequency curves. The forms are: 1. Symmetrical Unimodal Curve 2. Moderately Asymmetrical (Skew) Distribution 3. Extremely Skew (J- Shaped) 4. U-Shaped or Antimodal Curves. Form # 1. Symmetrical Unimodal Curve: Point of maximum in the middle and the curve is symmetrical on both sides. Form # 2. Moderately Asymmetrical (Skew) [...]
The mode is defined to be size of the variable which occurs most frequently or the point of maximum frequency or the point of maximum frequency or the point of greatest density. It is also an important measure of central tendency. For example, we have given the data, that is, 19, 21, 20, 19, 19, 19, 25, in this case, [...]
When the observations are arranged in ascending or descending order of magnitude, then the middle value is known as median of these observations. Let x1, x2 ....xn be n observations arranged in the ascending order of magnitudes. Median is defined as the 'middle most' term, that is, the value of x at the position n+1/2, i.e, we can write. Median [...]
Geometric mean is defined as the Nth root of the product of N items. For example, if we have two items then we will take square root, if we take three items then we take cube root and so on. It can be calculated from following formula: Where X1 X2 .... Xn = various items in a series n = [...]
Here is a compilation of top twenty-eight problems on the measures of central tendency along with its relevant solutions. Problem 1: Calculate the mean using different methods: Solution: (i) X̅ Under direct method X̅ = 3300/100 = 33 (ii) X̅ short-cut method X̅ = 25 + 800/100 = 25 + 8 = 33 100 (iii) X̅ under step deviation method [...]
Here is a compilation of top twenty-eight problems on the measures of central tendency along with its relevant solutions. Problem 1: A firm buys machinery worth Rs. 2,00,000 every year and writes off depreciation as given below: Find the average depreciation rate per year. Solution: Now, arranging the data for 3 parts, we find Calculation average depreciation rate: X̅w = [...]
Arithmetic Mean Calculations: Formula, Simple and Weighted Arithmetic Mean! In this article we will discuss about the calculation of simple and weighted arithmetic mean with the help of formulas. Arithmetic mean is a commonly used average to represent a data. It is obtained by simply adding all the values and dividing them by the number of items. Arithmetic mean can [...]
Median is the middle value in a distribution. It is a positional average. Median divides the data into equal halves, wherein 50 percent of the values lie below the median and 50 percent of the values lie above the median. Before determining the middle value, the observations have to be arranged in an ascending or descending order. Once the data [...]
Mode is the value that occurs with the greatest number of frequency. For example- if the given set of values are 2, 3, 2, 4, 5, 2, 3, 1, 6 the mode here would be 2 which appears thrice. However, when there are 2 or more values appearing with same frequencies then the mode is said to be ill-defined. Such [...]
In this article we will discuss about the relationship between mean, median and mode. Distribution of statistical data shows how often the values in the data set occur. A distribution is said to be symmetrical when the values of mean, median and mode are equal. That is, there is equal number of values on both sides of the mean which [...]