NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 3 - Organisation of Data
NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 3 - Organisation of Data Page/Excercise 38
The correct answer is option (a).
The class midpoint is the average value of the upper class limit and the lower class limit.
The correct answer is option (b).
The frequency distribution of two variables is known as Bivariate Frequency Distribution. This indicates a series of statistical data with two variables such as production and consumption of a particular product in the market.
The correct answer is option (d).
Statistical calculations in classified data are based on the class midpoints. This classified data or continuous series can take any numerical value, and hence, the class midpoint is used to represent the class.
The correct answer is option (a).
Under the exclusive method, the upper class limit of a class is excluded in the class interval. This is because the series which is the upper limit of one class interval is the lower limit of the next class interval.
The correct answer is option (a).
Range is the difference between the largest and smallest observations. This implies the variation in the values of variables.
Range = Highest value - Lowest value
Yes, there are advantages in classifying things. The following points highlight the advantages of classification:
- Simplification: Classification facilitates the arrangement of data in a presentable form which appears to be brief and simple for analysis.
- Effective: Classification enhances the usage of data as it brings out similarity within the diverse set of data. Thus, classification of things is more effective and saves time when searching for information from huge data.
For example, books in your school library are classified according to subjects as English, Mathematics, Science, Social Studies, GK and general story books. This enables students to refer to the particular subject book for detailed study. Thus, it saves the student's valuable time and effort during the course of study.
A characteristic which is measurable and changes its value over a period of time is called a variable. This implies that the quantity is subject to change and can be measured by a particular unit. For example, if we measure the age of students studying in Class VI which is subject to change, then the age of students is known as a variable.
Discrete Variable |
Continuous Variable |
A variable which can take only certain values. |
A variable which can take any value in a particular limit. |
It jumps from one value to another value, but it will not consider the intermediate value between two values. Thus, the value of the variables can increase in complete numbers. |
Its value increases in fractions but not in jumps. |
Examples: Number of students who opt for Commerce in Class 11, say 30, 35, 40, 45 and 50 |
Examples: Height, weight and age of family members; in weight, say 50 kg, 30 kg, 42 kg and 18 kg |
- Exclusive method: Under the exclusive method, every class interval excludes items corresponding to its upper limit. This is because the series in which the upper limit of one class interval is the lower limit of the next class interval. Hence, the continuity of data is maintained. This is more suitable for continuous variables. For example, consider a class interval 10-20. Here, values between 10 and 19 will be included and the value of the 20^{th} item will be included in the next class interval, i.e. 20-30.
- Inclusive method: Under the inclusive method, every class interval includes all items up to its upper limit. This is because the series in the upper limit of the class interval will not repeat itself as a lower limit of the next class interval. For example, 5-10, 11-15 and 16-20. Here, all the items ranging between 5 and 10 are included in that class interval, items ranging between 11 and 15 are included in that class and items ranging between 16 and 20 are included in that class interval.
- Calculation of range of monthly household expenditure on food:
Formula to calculate range is
Range = Highest value - Lowest value
Given that
Highest value = 5090
Lowest value = 1007
Therefore,
Range = 5090 - 1007 = 4083
- Frequency distribution of expenditure:
Given that the lowest monthly household expenditure is 1007 and the highest monthly household expenditure is 5090. The distribution of frequencies will relate to values between 1000 and 5500. Thus, the class interval will be 500.
- Based on the frequency distribution of expenditure:
- Number of monthly household expenditure on food is less than Rs 2000 = 20 + 13 = 33
- Number of monthly household expenditure on food is more than Rs 3000 = 2 + 1 + 2 + 0 + 1 = 6
- Number of monthly household expenditure on food is between Rs 1500 and Rs 2500 = 13 + 6 = 19
NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 3 - Organisation of Data Page/Excercise 39
Frequency array of the number of domestic appliances being used by households:
The frequency distribution summarises the raw data given by making it concise. However, it does not show the details which are found in the raw data and leads to loss of information. As the raw data is grouped into classes, an individual analysis has no significance for further statistical calculation. For example, Class 5-15 has 7 items for analysis (12, 14, 8, 10, 11, 13 and 7) as raw data. Here, the individual observation loses its significance for further statistical calculation because only frequency is recorded but not their actual values. All the values in each class are assumed to be equal to the middle value of the class interval. Statistical calculations are based on the values of the class interval instead of the actual values. Thus, the absence of actual values for analysis leads to loss of information.
Yes, classified data is better than raw data. This is because
- Simplification: Raw data are large and difficult to handle. On the other hand, classification facilitates the arrangement of data in a presentable form which appears to be brief and simple for analysis.
- Effective: Raw data is not easy to understand and cannot conclude any meaningful information for the study. On the other hand, classification enhances the usage of data as it brings out similarity within the diverse set of data. Thus, classification of things makes it more effective.
- Save time: Raw data is huge to search for particular information, whereas classified data saves time when searching for information.
Univariate Frequency Distribution |
Bivariate Frequency Distribution |
The word 'Uni' refers to one. |
The word 'Bi' refers to two. |
This implies a series of statistical information representing the frequency distribution of one variable. |
This implies a series of statistical information representing the frequency distribution of two variables such as production and sales of a particular product. |
Examples: Marks of a Class VI student, income of an individual in a particular area |
Example: Production and sales of a particular product |
Frequency distribution by the inclusive method taking class interval of 7.