Question 1

Which of the following is the first step in designing a statistical project according to the chapter 'Use of Statistical Tools'?

Accepted Answer

Identifying a problem or an area of study — The first step in designing a statistical project is to clearly identify the problem or area of study. This sets the objective for the project and guides all subsequent steps such as data collection and analysis.

Question 2

What is the importance of choosing an appropriate target group in a statistical project?

Accepted Answer

Choosing an appropriate target group is important because it helps in framing relevant questions for the questionnaire. For example, if the project is about cars, the target group would be middle and higher income groups. This ensures that the data collected is relevant and useful for the study. — The target group determines who will provide the data, so selecting the right group ensures that the data collected is representative and relevant to the problem being studied. It also helps in designing suitable questions for data collection.

Question 3

Which of the following methods is NOT a primary method of data collection?

Accepted Answer

Using data from government reports — Primary data collection involves first-hand collection methods such as interviews, postal surveys, phone, and email surveys. Using data from government reports is secondary data collection as it uses already existing data.

Question 4

Explain the difference between primary and secondary data with an example related to economic studies.

Accepted Answer

Primary data is first-hand data collected directly by the researcher, for example, conducting a survey on consumer preferences for toothpaste. Secondary data is data collected by someone else, such as using government census reports or research papers for studying literacy rates. — Primary data collection involves direct interaction with respondents and is specific to the study's objectives, while secondary data is pre-existing data collected for other purposes but can be used if it suits the research needs.

Question 5

Which of the following diagrams is NOT mentioned in the chapter as a tool for data presentation?

Accepted Answer

Scatter plot — The chapter mentions bar diagrams, pie diagrams, and histograms as tools for organizing and presenting data. Scatter plots are not mentioned in this chapter.

Question 6

What statistical measures are used to analyze the average, variability, and relationship among variables in a project?

Accepted Answer

Measures of Central Tendency such as mean are used to find the average, Measures of Dispersion such as standard deviation are used to measure variability, and Correlation is used to find the relationship between variables. — These statistical tools help summarize data by indicating central values, spread of data, and the strength and direction of relationships between variables, which are essential for interpretation.

Question 7

Why is it important to include a bibliography section in a project report?

Accepted Answer

A bibliography section is important because it lists all the secondary sources such as magazines, newspapers, and research reports used in the project, giving credit to original authors and allowing readers to verify sources. — Including a bibliography ensures transparency, avoids plagiarism, and provides a reference for further study or verification of the information used in the project.

Question 8

As a marketing manager, you want to study the effect of advertisements on the sales of a consumer product. Which step in the project design process would help you decide the target group for your study?

Accepted Answer

Choice of target group — After identifying the problem, choosing the appropriate target group is essential to frame relevant questions and collect data from the right segment of consumers affected by advertisements.

Question 9

Fill in the blank: The method of data collection which requires observations to be taken on all individuals in a population is called the _____ method.

Accepted Answer

Census Method — The Census Method involves collecting data from every individual in the population, ensuring complete coverage without sampling.

Question 10

What is the assumed mean method used for in statistical calculations?

Accepted Answer

The assumed mean method is used to simplify the calculation of mean by taking an approximate value as the mean and calculating deviations from it. — This method reduces computational complexity by using a convenient value as the mean and adjusting calculations accordingly, especially useful for grouped data.

Question 11

Calculate the mean monthly family income given the following frequency distribution and using the assumed mean method:

| Income Class (Rs) | Midpoint (x) | Frequency (f) |
|-------------------|--------------|---------------|
| 0-10,000          | 5,000        | 20            |
| 10,000-20,000     | 15,000       | 40            |
| 20,000-30,000     | 25,000       | 30            |
| 30,000-40,000     | 35,000       | 10            |

Assume the mean (A) = Rs 20,000 and class width (c) = Rs 5,000.

Use the formula: $\overline{X} = A + \frac{\sum f d'}{\sum f} 	imes c$, where $d' = \frac{x - A}{c}$.

Accepted Answer

Rs 18,000 — Given: 
Income classes and frequencies as in the table.
Assumed mean A = 20,000
Class width c = 5,000

Calculate d' for each class:
0-10,000: d' = (5,000-20,000)/5,000 = -3
10,000-20,000: d' = (15,000-20,000)/5,000 = -1
20,000-30,000: d' = (25,000-20,000)/5,000 = 1
30,000-40,000: d' = (35,000-20,000)/5,000 = 3

Calculate fd':
20×(-3) = -60
40×(-1) = -40
30×1 = 30
10×3 = 30
Sum fd' = -60 - 40 + 30 + 30 = -40

Total frequency = 100

Mean $\overline{X} = 20,000 + \frac{-40}{100} 	imes 5,000 = 20,000 - 2,000 = 18,000$ Rs

Answer: Rs 18,000

Question 12

What is the significance of calculating standard deviation in a statistical project?

Accepted Answer

Standard deviation measures the variability or dispersion of data around the mean. It helps understand how spread out the data points are, indicating consistency or diversity in the data. — By calculating standard deviation, one can assess the reliability of the mean and the extent of variation in the data, which is crucial for interpreting results accurately.

Question 13

Using the following data, calculate the standard deviation of monthly family income:

| Income Class (Rs) | Frequency (f) | d' = (X - 20,000)/5,000 | fd' | fd'^2 |
|-------------------|---------------|-------------------------|------|-------|
| 0-10,000          | 20            | -3                      | -60  | 180   |
| 10,000-20,000     | 40            | -1                      | -40  | 40    |
| 20,000-30,000     | 30            | 1                       | 30   | 30    |
| 30,000-40,000     | 10            | 3                       | 30   | 90    |
| Total             | 100           |                         | -40  | 340   |

Use the formula: $\sigma = \sqrt{\frac{\sum f d'^2}{\sum f} - \left(\frac{\sum f d'}{\sum f}ight)^2} 	imes c$ where $c = 5,000$.

Accepted Answer

Rs 9,000 — Given:
Sum fd' = -40
Sum fd'^2 = 340
Total frequency = 100
Class width c = 5,000

Calculate variance:
= (340/100) - (-40/100)^2
= 3.4 - 0.16
= 3.24

Standard deviation $\sigma = \sqrt{3.24} 	imes 5,000 = 1.8 	imes 5,000 = 9,000$ Rs

Answer: Rs 9,000

Question 14

Which of the following occupations had the highest number of families surveyed in the toothpaste project?

Accepted Answer

Trader — According to the data, traders accounted for 40 families, which is the highest among the listed occupations.

Question 15

Analyze the following observation from the toothpaste project: "Pepsodent, Colgate, and Close-up were the most preferred brands." What factors influenced this preference according to the data?

Accepted Answer

The preference for Pepsodent, Colgate, and Close-up was influenced mainly by standardised markings, quality, price, and company's brand name as these features had the highest number of family members selecting toothpaste based on them. — The data shows that consumers chose toothpaste brands based on quality, price, brand reputation, and standardised markings, indicating trust and perceived value in these brands.

Use of Statistical Tools

Use of Statistical Tools — Study Notes

INTRODUCTION

Steps Towards Making a Project

SUGGESTED LIST OF PROJECTS

Practice Questions — Use of Statistical Tools

All 8 Chapters in Statistics for Economics