Arithmetic Mean

The arithmetic mean is defined as the total sum of observations divided by the total number of observations. Here we study about the arithmetic mean of continuous series. Calculation of arithmetic means in continuous series When the number of items is large, we have to divide them into groups. Such groups are known as simple classes. It should be noted that there is no gap between any two successive intervals. So the data is continuous and the series is called continuous series.

Summary

The arithmetic mean is defined as the total sum of observations divided by the total number of observations. Here we study about the arithmetic mean of continuous series. Calculation of arithmetic means in continuous series When the number of items is large, we have to divide them into groups. Such groups are known as simple classes. It should be noted that there is no gap between any two successive intervals. So the data is continuous and the series is called continuous series.

Things to Remember

Arithmetic Mean can be calculated in three different methods.

  1. \(Direct \: method, \overline{X} = \frac{\sum fm}{n}\), where m is the mid-value of class intervals.
  2. \(Short \: cut \: method,\overline{X} = A + \frac{\sum fd}{n} \), where d= X - A and A is assumed mean.
  3. \(Step \: deviation \: method, \overline{X} = A + \frac{\sum fd'}{n}\) \( \times h \), where d' = \(\frac{d}{h}\) and h is the length of class interval.

MCQs

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Subjective Questions

Q1:

What are the major sources of population data? Mention.


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>The major sources of population data are primary data and secondary data.</p>
<ol>
<li><strong>Primary data</strong><br />Primary sources are obtained by witnesses or recorders who experienced the events or conditions being documented. Primary sources can also include autobiographies, memoirs, and oral histories recorded later. Primary sources of data may be:<br />
<ul>
<li>Sample surveys</li>
<li>Census</li>
<li>Vital Registration</li>
<li>Administrative Records</li>
</ul>
</li>
<li><strong>Secondary data</strong><br />Secondary data refers to data that was collected by someone other than the user. Secondary sources of statistics can be journals, magazines, reports related to different researchers, annual reports etc.</li>
</ol>

Q2:

Define census and vital registration.


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>A population census determines the size of a country's population and the characteristics of its people, such as their sex, background, marital status and income,literacy, religion, language, caste/ethnic group, economically active population, education, number of children, employment status, occupation etc.</p>
<p>The most common way of collecting information on these events is through Vital Registration. It is the administrative system used by the governments to record vital events which occur in their populations. It also refers to the formal registration and statistical recording of vital events such as birth, death, migration, marriage, abortion, divorce and adoption.</p>

Q3:

 What is Sample Survey?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Sample Survey is the process of selecting a sample of elements from a target population to conduct a survey. The term survey may refer to many different types or techniques of observations. The survey sampling most often involves a questionnaire used to measure the characteristics and attitudes of people. It is the process of collecting important data from a selected groups of people that represent the whole population of an area.</p>

Q4:

What are administrative records?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Administrative records are very vital for an effective plan to manage the population. The administrative records are the paper trail that documents the agency's decision-making process and the basis for the agency's decision. It is a data collected by administrative units like number of students, telephone directory, records of public servants, health status etc.</p>

Q5:

What was the total population of Nepal in 2011?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>The total population of Nepal in 2011 was 2,64,94,504.</p>

Q6:

When was the first census taken in Nepal?


Type: Short Difficulty: Easy

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Answer: <p>The first census was taken in 1911 A.D. in Nepal.</p>

Q7:

What is the main source of population data?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>The main source of population data is census.</p>

Q8:

What are the primary sources of data?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>The primary sources of data are as follows:</p>
<ul>
<li>Vital Information</li>
<li>Census</li>
<li>Sample Surveys</li>
<li>Administrative Records</li>
</ul>

Q9:

Write the examples of secondary data.


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Secondary data are those data which are already prepared and compiled by different national and international organizations for their own purpose. Secondary sources of statistics can be journals, magazines, reports related to different research, annual reports etc. Secondary data can be obtained from different sources such as</p>
<ul>
<li>progress reports</li>
<li>internet searches or libraries</li>
<li>information collected through censuses or government departments like housing, social security, electoral statistics, tax records etc.</li>
</ul>
<p>&nbsp;</p>

Q10:

 What are major sources of population data?


Type: Very_short Difficulty: Easy

Show/Hide Answer
Answer: <p>The major sources of population data are Census, Vital Registration, Sample Surveys etc.</p>

Q11:

What is a census?


Type: Very_short Difficulty: Easy

Show/Hide Answer
Answer: <p>A census is a term usually referred to an official count by a national government of country's population in every 10 years.</p>

Videos

Sources of Population Statistics
Sources of Population Statistics
Sources of Population Statistics
Sources of Population Statistics
Sources of Population Statistics
Arithmetic Mean

Arithmetic Mean

The word "statistics " refers two meanings. In the singular sense, it deals with the collection, presentation, analysis and interpretation of numerical data and helps in making a decision. In the plural sense, it refers to the numerical facts and figures are sometimes known as statistical data.

Measures of central tendency

.

A typical value which represents the characteristics of the entire mass of huge data is called the central value of the whole distribution. A measure of the central tendency is also known as a measure of location or an average.
The various measure of central tendency are as follow:

  1. Arithmetic Mean (average)
  2. Median
  3. Mode

Arithmetic Mean

The arithmetic mean is defined as the total sum of observations divided by the total number of observations. Here we study about the arithmetic mean of continuous series.

Calculation of arithmetic means in continuous series

When the number of items is large, we have to divide them into groups. Such groups are known as simple classes. It should be noted that there is no gap between any two successive intervals. So the data is continuous and the series is called continuous series.

Arithmetic Mean can be calculated in three different methods.

  1. \(Direct \: method, \overline{X} = \frac{\sum fm}{n}\), where m is the mid-value of class intervals.
  2. \(Short \: cut \: method,\overline{X} = A + \frac{\sum fd}{n} \), where d= X - A and A is assumed mean.
  3. \(Step \: deviation \: method, \overline{X} = A + \frac{\sum fd'}{n}\) \( \times h \), where d' = \(\frac{d}{h}\) and h is the length of class interval.


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Lesson

Statistics

Subject

Compulsory Mathematics

Grade

Grade 10

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