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NCERT Class 11 Economics Chapter 3 Organisation of Data
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Organisation of Data
Chapter: 3
PART – (A) STATISTICS FOR ECONOMICS
TEXTUAL QUESTION ANSWERS
1. Which of the following alternatives is true?
(a) The class midpoint is equal to:
(i) The average of the upper class limit and the lower class limit.
(ii) The product of the upper class limit and the lower class limit.
(iii) The ratio of the upper class limit and the lower class limit.
(iv) None of the above.
Ans: (i) The average of the upper class limit and the lower class limit.
(b) The frequency distribution of two variables is known as:
(i) Univariate Distribution.
(ii) Bivariate Distribution.
(iii) Multivariate Distribution.
(iv) None of the above.
Ans: (ii) Bivariate Distribution.
(c) Statistical calculations in classified data are based on:
(i) The actual values of observations.
(ii) The upper class limits.
(iii) The lower class limits.
(iv) The class midpoints.
Ans: (i) The actual values of observations.
(d) Range is the:
(i) Difference between the largest and the smallest observations.
(ii) Difference between the smallest and the largest observations.
(iii) Average of the largest and the smallest observations.
(iv) Ratio of the largest to the smallest observation.
Ans: (i) Difference between the largest and the smallest observations.
2. Can there be any advantage in classifying things? Explain with an example from your daily life.
Ans: The various advantages of classification are:
(a) It helps in comparison of data.
(b) It helps us to understand the relationship among variables.
(c) It highlights significant features of the data at a glance.
(d) It makes the statistical analysis of the data easier.
(e) It arranges and presents huge volumes of raw data in meaningful and condensed form.
In our daily life, we classify our set of clothes item wise in our almirahs so that they can be easily located.
3. What is a variable? Distinguish between a discrete and a continuous variable.
Ans: A measurable characteristic whose value changes overtime is called variable. It refers to that quantity which keeps on changing and which can be measured by some unit. For example, if we measure the height of students of a class, then height is regarded as a variable.
| Basic | Discrete Variable | Continuous Variable |
| Meaning | A discrete unit is a separate part of something larger. A room is a discrete space within a house, just as the crankshaft is a discrete part of a car engine. | The exact age is a continuous variable, but age is often rounded down to the closest integer. In this case, it would be a discrete variable. |
| Values | Values are obtained by counting. | Values are obtained by measuring. |
| Examples | Number of students in a class, number of red marbles in a jar etc. | Height of students in a class, weight of students in a class etc. |
4. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data.
Ans: There are two methods of classifying data according to class intervals, named as exclusive method and inclusive method.
Exclusive Method: In this method, the classes are formed in such a way that the upper class limit of one class becomes the lower class limit of the next class. Continuity of the data is maintained in this method. The upper limit is excluded but the lower limit is included in the class interval. This method is most appropriate for data of continuous variables.
Inclusive Method: Under this method of classification of data, the classes are formed in such a manner that the upper limit of a class interval does not repeat itself as the lower limit of the next class interval. In such a series, both the upper limit and the lower limit are included in the particular class interval, for example, 1–5, 6–10, 11–15 and so on. The interval 1–5 includes both the limits i.e. 1 and 5.
5. Use the data in Table 3.2 that relate to monthly household expenditure (in ₹) on food of 50 households.
(a) Obtain the range of monthly household expenditure on food.
(b) Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure.
(c) Find the number of households whose monthly expenditure on food is
(i) Less than ₹2,000
(ii) More than ₹3,000
(iii) Between ₹1,500 and ₹2,500
Table 3.2
Ans: (a) Range = Largest Value – Smallest Value = 5,500-1,007 = 4,083
(b)
(c) (i) Number of households whose monthly expenditure on food is less than ₹2000 = 20 + 13 = 33
(ii) Number of households whose monthly expenditure on food is more than ₹3000 = 2 + 1 + 2 + 0 + 1 = 6
(iii) Number of households whose expenditure on food is between ₹1500 and ₹ 2500 = 13 + 6 = 19
6. In a city 45 families were surveyed for the number of Cell phones they used. Prepare a frequency array based on their replies as recorded below.
| 1 | 3 | 2 | 2 | 2 | 2 | 1 | 2 | 1 | 2 | 2 | 3 | 3 | 3 | 3 |
| 3 | 3 | 2 | 3 | 2 | 2 | 6 | 1 | 6 | 2 | 1 | 5 | 1 | 5 | 3 |
| 2 | 4 | 2 | 7 | 4 | 2 | 4 | 3 | 4 | 2 | 0 | 3 | 1 | 4 | 3 |
Ans: Frequency Array
| No. Of Domestic Appliances | No. Of Households |
| 0 | 1 |
| 1 | 7 |
| 2 | 15 |
| 3 | 12 |
| 4 | 5 |
| 5 | 2 |
| 6 | 2 |
| 7 | 1 |
| Total | 45 |
7. What is ‘loss of information’ in classified data?
Ans: The frequency distribution summarises the raw data by making it concise and comprehensible. The classification or grouping of raw data into classes makes it more concise and understandable. But simultaneously there exists a loss of information. The calculations involved in the classified data or the continuous series are based on the class midpoints. The items in such series cannot be exactly measured and consequently, an individual observation loses its importance during the statistical calculations. Statistical calculations are based only on the values of class marks instead of the actual values.
8. Do you agree that classified data is better than raw data? Why?
Ans: Classified data is better than raw data because classification of data involves conversion of raw data into statistical series in a manner such that some meaningful conclusions can be drawn out of them. Classification makes the raw data comprehensible by summarising them into groups.
9. Distinguish between univariate and bivariate frequency distribution.
Ans:
| Basic | Univariate Frequency Distribution | Bivariate Frequency Distribution |
| Meaning | In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables). | Bivariate frequency distribution refers to a series of statistical data with two variables like the data on income as well as savings of the households. We also learned that bivariate data involves relationships between the two variables, while univariate data involves describing the single variable. |
| Aims | The main goal of univariate data is to describe the data using mean, median, variance, mode, dispersion, range, standard deviation, etc. | The bivariate distribution are statistical methods used to show the probability of two random variables occurring. |
| Alternate name | In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables). | A bivariate distribution (or bivariate probability distribution) is a joint distribution with two variables of interest. The bivariate distribution gives probabilities for simultaneous outcomes of the two random variables. |
| Examples | Height of students in a class. | Height and weight of students in a class. |
10. Prepare a frequency distribution by inclusive method taking class interval of 7 from following data.
Ans:
11. “The quick brown fox jumps over the lazy dog”. Examine the above sentence carefully and note the numbers of letters in each word. Treating the number of letters as a variable, prepare a frequency array for this data.
Ans: Frequency Array
| No. Of Letters | No. Of Alphabets |
| 1 | 3 |
| 2 | 5 |
| 3 | 5 |
| 4 | 3 |
| 5 | 5 |
| 6 | 4 |
| 7 | 3 |
| 8 | 4 |
| 9 | 3 |
| Total | 35 |
