Sample Statistic: Overview, Questions, Preparation

Statistics 2021 ( Statistics )

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Rachit Kumar Saxena

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 13, 2021 14:11 IST
What is Sample Statistics?

Sample Statistics is defined as any figure calculated from your sample data, for example, sample average, sample standard deviation, median, and percentiles. However, whenever your statistical data like median, median, or any other statistics comes from a fraction of information and part of a population is known as Sample Statistics. 

Sample Statistics

Sample Statistics Formula 

Here are the formulas of sample statistics for mean, and the standard deviation is as follows: 

Sample Standard Deviation Formula 

The standard deviation of the small sample statistics is calculated using the formula √(∑(xi−x̄)2/n). In order to obtain an unbiased estimation of the sample standard deviation, the n is the numerator, which is replaced by n-1 so that the formula will be: 

Sample SD

Sample Mean Formula 

The calculation of the Sample Mean is a little bit different from calculating the population mean. In order to compute the Sample mean, we just have to add all the data values and divide this substitution by the number of figures present in the data set. Thus, the Sample mean is as follows: 

Sample Stats_2

Symbols of Sample Statistics 

There are various symbols that are used of sample statistics for parameters, and statistics are as follows 

Characteristic

Sample Statistic

Population Parameter

Mean

μ

Standard deviation

s

σ

Proportion

p^

p

Sample Stats_Formulae

Weightage of Sample Statistics

Sample Statistics is a topic from the chapter Statistics. The chapter has weightage around 9 to 11 marks in class X. Aspirants are facing around 3 to 4 questions of statistics in the examination every year. Statistics is also a part of class XI, XI, and XII. Apart from Sample Statistics, there are also various other significant topics covered in this chapter, such as: 

  • Sample Standard Deviation 
  • Mean
  • Median
  • Mode 

Illustrative Examples on Sample Statistics

1. The following are the GPA scores of 30 secondary institutions. Find out the sample mean.3.1, 2.9, 2.8, 2.9, 3.8, 4.8, 4.2, 3.9, 3.4, 2.5, 4.2, 3.7, 3.3, 2.1, 3.8, 3.0, 3.7, 4.0, 2.7, 3.8, 3.2, 3.5, 3.5, 3.6, 2.2, 3.1, 3.5, 4.0, 2.7, 4.5.

Solution:

Using the given below formula to compute sample mean: 

Sample Stats_4

= (102.4/30)
= 3.41 
Thus, the Sample mean is 3.41

2.Some students' total marks in science examinations are 101, 161, 155, 96, and 33. Find out the Sample mean marks. 

Solution:

Sample Stats_4

x̄ = 101+161+155+96+33/5
x̄ = 119.2 
Hence, the sample marks are 119.2.

FAQs on Sample Statistics

Q: What is Statistics? 

A: Statistics is one of the modes of mathematical analysis that is using representations, synopses, quantified models for a given set of real-life studies and experimental data. 

Q: What is Sample Statistics? 

A: In Statistics methodology, sample statistics are defined as information that you obtain from a fraction of the population. For example, a sample average, sample standard deviation, percentile, and median. 

Q: How do you find Sample Statistics? 

A: The following are the basic steps that will help you to calculate the sample average of a data set as follows: 
  1. Make the addition of all sample items. 
  2. Divide sum by the number of samples you have. 
  3. As a result, you will get mean. 
  4. After that, use that means to find a variance. 
  5. Now, Use the variance to find the standard deviation. 

Q: What is the usage of Sample Mean? 

A: Sample Mean is mainly calculated to analyze central tendency, the variance of a data set, or standard deviation of a data set. It can be applied to several uses, such as calculating population averages. 

Q: What is the formula of Sample Mean and sample standard deviation? 

A: The formula to calculate Sample mean and sample standard deviation is as follows: 
Sample Stats_Formulae_2.JPG

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