Statistics, Frequency and Frequency Distributions

Statistics: - By “statistics” we mean aggregate or combination of facts affected to a marked extends by multiplicity of causes, numerically expressed and estimated according to reasonable standards of accuracy, collected in a systematic manner and placed in relation to each other.

There are two ways of statistics:

1. Frequency Distribution and

2. Graphical Distribution.

Frequency: - The way to count the number of items a particular value is repeated, is called the frequency of any class.

That means, frequency is the total number of items that a particular value is repeated in a table or data.

Frequency Distributions: - A set of classes together with the frequencies of occurrence of values in again set of data, presented in a tabular form, is referred to as a frequency distribution.

frequency distribution

Construct a frequency distribution from the class marks of EEE 36 Batch who got the numbers in total trimester in statistics and probability.

Course:

97, 13, 81, 25, 37, 55, 19, 33, 59, 46, 67, 43, 12, 87, 90, 65, 76, 81, 79, 13, 5, 12, 35, 17, 46, 65, 43, 12, 85, 93,

Solution:

Here, the lowest value=5

And the highest value=97

For this kind of ungrouped data we have to choose k in such a way that 2k ≥ number of variables.

Here, k=5

So 2k = 25 = 32 > 30

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Graphical Distribution of Frequency Distribution

Frequency distribution can be presented graphically in any one of the following ways: Histogram Frequency Polygon Smooth Frequency Curve Cumulative Frequency Curve of Ogive Curve Pie-Chart Histogram: - A histogram is an area diagram in which the frequencies corresponding to each class interval of frequency distribution are by the area of a rectangle without leaving no gap between the cosective rectangles. Frequency Polygon: - This is one kind of histogram which is represented by joining the straight lines of the mid points of the upper horizontal side of each rectangle with adjacent rectangles. Smooth Frequency Curve: - This is one kind of histogram which is represented by joining the mid points by free hand of the upper horizontal side of each rectangle with adjacent rectangles. Comulative Frequency Curve or Ogive Curve: - The total frequency of all values less then the upper class boundary of a...

Empirical Relation between Mean, Median and Mode

A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution. Conversely, when values of mean, median and mode are not equal the distribution is known as asymmetrical or skewed distribution. In moderately skewed or asymmetrical distribution a very important relationship exists among these three measures of central tendency. In such distributions the distance between the mean and median is about one-third of the distance between the mean and mode, as will be clear from the diagrams 1 and 2 Karl Pearson expressed this relationship as:

Correlation and Linearity

Correlation coefficients measure the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient , measures the strength of the linear association between variables. In this tutorial, when we speak simply of a correlation coefficient, we are referring to the Pearson product-moment correlation. Generally, the correlation coefficient of a sample is denoted by r , and the correlation coefficient of a population is denoted by ρ or R . How to Interpret a Correlation Coefficient The sign and the absolute value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables. The value of a correlation coefficient ranges between -1 and 1. The greater the absolute value of a correlation coefficient, the stronger the linear relationship. The str...

Poisson Distribution

A Poisson experiment is a statistical experiment that has the following properties: The experiment results in outcomes that can be classified as successes or failures. The average number of successes (μ) that occurs in a specified region is known. The probability that a success will occur is proportional to the size of the region. The probability that a success will occur in an extremely small region is virtually zero. Note that the specified region could take many forms. For instance, it could be a length, an area, a volume, a period of time, etc. Notation The following notation is helpful, when we talk about the Poisson distribution. e : A constant equal to approximately 2.71828. (Actually, e is the base of the natural logarithm system.) μ: The mean number of successes that occur in a specified region. x : The actual number of successes that occur in a specified region. P( x ; μ): The Poisson probability that exactly x ...

Statistics & Probability

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