Sample Size: Overview, Questions, Preparation

This chapter has multiple topics listed below:

Statistics Standard Deviation Correlation Bar Graph Chi Square Test Measures of Central Tendency Variance Extrapolation Null Hypothesis Pareto Chart Harmonic Mean How to find Median Statistics Definition Data Collection Methods Frequency Polygons Central Tendency Confidence Interval Data Handling Statistical Inference Quota Sampling Interquartile Range Quartiles Variance and Standard deviation Cluster Analysis Correlation and Regression Graphical Representation Least Square Method Level of Significance Paired T Test Z Score Table Assumed Mean Method Box and Whisker Plot Gamma Distribution Sample Size T Distribution Tests of Significance Types of Statistics Continuous Variable Sample Statistic Exponential Smoothing T Test Table Bivariate Analysis Relative Frequency Difference between Average and ...Difference between Mean and Med...Difference between Parametric a...Grouping data Statistics pdf Mean Absolute Deviation Population and Sample

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 5, 2021 10:33 IST

Table of Contents

What is Sample Size?
Weightage of Sample Size in class 11
Illustrative Example on Sample Size
FAQs on Sample Size

What is Sample Size?

For research, survey, or experiment a set of data is taken into account. The branch of mathematics that deals with a set of data and their operations is known as statistics.

The sample size is generally used for selecting the number of observations to analyse the given statistical data. Selecting a sample size is a critical part of any study to make inferences about the given elements from a given sample.

The statistical data is majorly classified into population data and sample data. Population data includes the entire area of study. The sample data is a part of the population data that represents the entire set.

The sample size is interpreted as the number of measurements used to determine the evaluation of a population. The dimension of the sample is extracted directly from the population set.

Sampling is the method of election of a subset of quantifiers from the entire population, to evaluate the features of the aggregate population. A fraction of entities in a subset of a population is chosen for analysis.

The formula to determine the sample size of a population is-

S_s= {Z²P(1- P)}/C².

In this formula, S_s denotes the sample size, Z denotes the Z-factor, P represents the percentage of a population, and C denotes the interval confidence.

The mean of a population gives a value of the average quantity in the entire population interval. The mean of a sample of this population gives the average value for that particular sample set. The mean value of the sample may vary from the population mean. This difference is known as a deviation or error.

The error E in a sample mean is calculated using the formula-

Weightage of Sample Size in class 11

The topic- the sample size is a part of the section- statistics in the syllabus of class 10 and 11. The chapter- collection of data includes this topic in class 11 economics. It carries a weightage of around 5-6 marks in the examination.

Illustrative Example on Sample Size

1. P is to create a one-sample z interval to estimate what proportion of her neighbourhood favour the construction of a park. The confidence level should reach above 95% and the error allowed is 2%. Determine the smallest sample size.

Solution:

So the smallest sample size to consider to get an error of less than 2% with a confidence level above 95% is 2401.

FAQs on Sample Size

Q: What is statistics?

A: Statistics is the branch of mathematics that deals with the collection and organization of data to draw inferences from its summary.

Q: What is the sample size?

A: The sample size is the measure of the count of samples required to carry out a study. It is a small part of a large population that represents the entire set.

Q: What is a small sample size?

A: If the size of the sample is tiny, it is tough to examine the data. The t-distribution is implemented to deal with a small amount of data.

Q: What is a large sample size?

A: If the number of quantities in a sample is significantly higher than the average count, it is known as a large sample size.

Q: What influences the sample size?

A: Measurements of the population, error margin, standard deviation, and the extent of confidentiality are some of the factors that influence the sample size.