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**Page No 38:**

**Question 1(i): The class midpoint is equal to:(a) The average of the upper class limit and the lower class limit.(b) The product of upper class limit and the lower class limit.(c) The ratio of the upper class limit and the lower class limit.(d) None of the above.Answer:** The option (a) is correct.

The class midpoint is equal to the average of the upper class limit and the lower class limit. It is known by adding the values of upper and lower limits and dividing the total by 2.

(a) Univariate Distribution

(b) Bivariate Distribution

(d) None of the above

The frequency distribution of two variables is known as Bivariate Frequency Distribution. In other words, Bivariate Frequency Distribution shows the series of statistical data having frequencies of two variables such as the data on income and expenditure of the households.

(a) the actual values of observations

(b) the upper class limits

(c) the lower class limits

(d) the class midpoints

The calculations in classified data or continuous series are based on the class midpoints. The items in a continuous series cannot be exactly measured. Consequently, the class midpoints are calculated.

(a) the upper class limit of a class is excluded in the class interval

(b) the upper class limit of a class is included in the class interval

(c) the lower class limit of a class is excluded in the class interval

(d) the lower class limit of a class is included in the class interval

A series in which upper limit of one class becomes the lower limit of the succeeding class interval is called exclusive series. In such series, the frequencies of the lower limit are included in that particular class whereas the frequencies of the upper limit are excluded.

(a) difference between the largest and the smallest observations

(b) difference between the smallest and the largest observations

(c) average of the largest and the smallest observations

(d) ratio of the largest to the smallest observation

Range is defined as the difference between the largest and the smallest observations.

Algebraically,

R = H â€“ L

Where,

R denotes range

H is the highest value

L is the lowest value

The advantage of classification can be better understood with the help of a daily life example. A post office on the regular basis sorts letters and then classifies them according to various attributes. Letters are classified first according to the states, then according to the cities and streets. Thus, this process of classification helps the postman to deliver posts quickly, efficiently and in a non-haphazard manner.

Answer:

Inclusive Methodâ€“ 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, 1â€“5, 6â€“10, 11â€“15 and so on. The interval 1â€“5 includes both the limits i.e. 1 and 5.

Range = Highest Value â€“ Lowest Value

Highest Value = 5090

Lowest Value = 1007

So, Range = 5090 â€“ 1007 = 4083

(a) less than Rs 2000

(b) more than Rs 3000

(c) between Rs 1500 and Rs 2500

a) Number of households whose monthly expenditure on food is less than Rs 2000

= 20 + 13 = 33

b) Number of households whose monthly expenditure on food is more than Rs 3000

= 2+1+2+0+1 = 6

c) Number of households whose monthly expenditure on food is between Rs 1500 and Rs 2500

= 13 + 6 = 19

**Question 6: In a city 45 families were surveyed for the number of domestic appliances they used. Prepare a frequency array based on their replies as recorded below.****Answer:** Frequency Array of appliances being used by households**Question 7: What is â€˜loss of informationâ€™ in classified data?****Answer:** â€˜Loss of informationâ€™ is a major drawback of the classified data. The classification or grouping of raw data into classes makes it more concise and understandable. But simultaneously there exists 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. Further, the statistical calculations are based on the values of the class marks, ignoring the exact observations of the data leading to the problem of loss of information.**Question 8: Do you agree that classified data is better than raw data?****Answer: **The classified data has following advantages over the raw data.**1. ****Comprehensive-** Raw data are large and entangled, whereas classified data are comprehensive and easily manageable.**2.** **Quick Information-** It is troublesome to pick up information from unclassified data. **Information can be easily collected from the classified data.3.**

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