Very Short Answer Type Questions
Q.1. What do you mean by central tendency?
Ans. A central tendency refers to a average or representative value of a statistical series.
Q.2. In how many parts is statistical average divided?
Ans. Statistical average is divided into two parts:
(i) Mathematical average
(ii) Positional average
Q.3. What are the types of positional average?
Ans. The different types of positional average are:
(i) Median
(ii) Mode
(iii) Partition values – quartiles, deciles and percentiles
Q.4. State the main functions of averages.
Ans. The following are the main functions of averages:
(i) Facilitate Comparisons: Averages make the whole series easy and definite thereby facilitating comparison. For example, by comparing average per capita income of different countries, the countries with the highest and lowest economic growth can be identified.
(ii) Help in the Formulation of Policies: Averages help in the formulation of policies. For example, if the government finds low level of literacy in certain areas, it can formulate appropriate policies to improve educational services.
(iii) Form the Basis for Statistical Analysis: The results derived from calculation of averages can easily be utilised to conduct statistical analysis and draw inferences.
(iv) Represent the Whole Series: Averages represent the series as a whole.
Q.5. State the properties of an ideal average.
Ans. The following are the main properties of an ideal average:
(i) Easy to Compute and Understand: The process of calculation of average should be simple and easy. If the calculation involves complex mathematical processes, it will not be readily understood. As a result, its use will be confined only to experts.
(ii) Rigid Definition: An average left to the observation of the investigator would be bias and hence, cannot represent the entire series. A rigidly defined average would always result in a definite figure.
(iii) Represent the Whole Series: It should be based on all the observations of the series. If some of the items of the series are ignored in the calculation, the average cannot be said to be a representative one.
(iv) Open to further Algebraic Treatment: If an average is not capable of further algebraic treatment, its use would be very limited.
(v) Not Affected by Sampling Fluctuations: The averages of two independent sample studies in any particular field should not differ much from each other. The averages with least fluctuation of sampling are considered better than those with more difference.
Q.6. Define Arithmetic mean
Ans. Arithmetic mean is the sum total of all the observations divided by the number of observations.
Q.7. State the types of arithmetic mean.
Ans. There are two types of arithmetic mean:
(i) Simple arithmetic mean
(ii) Weighted arithmetic mean
Q.8. What is weighted arithmetic mean?
Ans. Weighted arithmetic mean is the mean calculated on the basis of weights assigned to the various items, according to their relative importance.
Q.9. What are the merits of arithmetic mean?
Ans. The following are the merits of arithmetic mean:
(i) Arithmetic mean is the simplest of all averages. It is easy to understand and calculate.
(ii) Arithmetic mean is dependent on all the items of a series so it represents the whole series.
(iii) It is a stable average as it is not influenced by the fluctuations of samples.
(iv) Arithmetic mean has various algebraic features so that it can be used in higher statistical analysis.
(v) Arithmetic mean is a definite number and not an estimate.
(vi) Groups can be compared with the help of arithmetic mean.
(vii) Accuracy of arithmetic mean can be checked.
Q.10. What are the demerits arithmetic mean?
Ans. The following are the demerits of arithmetic mean:
(i) Extreme values cause huge variation of central value from certain observations in the series such that the arithmetic mean no longer represents the whole series.
(ii) It sometimes gives unrealistic results such as the average number of children in a family as 4.5, which is not possible. Value of mean is such that it is not a value from series like average of 2, 3, 7 would be 4 which is not in the series.
(iii) Arithmetic mean is suitable only for quantitative data.
(iv) It is not suitable for ratio, rate or percentage study.
Q.11. Write a short note on weighted arithmetic mean.
Ans. Weighted arithmetic mean is the mean calculated on the basis of weights assigned to the various items, according to their relative importance. For example, a person spends his entire income on items such as food (f), clothes (c) and entertainment (e). The arithmetic mean will be (f + c + e)/3. However, he may want to give more importance to food. For this, he may use as ‘weights’ the amount of food (q_{1}), the amount of clothes (q_{2}) and the amount of entertainment (q_{3}). Hence, the arithmetic mean weighted by the quantities would be (fq_{1} + cq_{2} + eq_{3})/(q_{1 }+ q_{2} + q_{3}).
Q.12. State the important features of median.
Ans. Median has the following features:
(i) It is easy to understand and compute.
(ii) It is not affected by extreme values.
(iii) It is a definite and clear average.
(iv) It can also be determined graphically.
(v) Since it is among the values of the series, it is a real value.
(vi) Median can also be determined easily in openend series.
Q.13. What are the demerits of median?
Ans. The following are the demerits of median:
(i) It lacks algebraic characteristics as it cannot be used in further mathematical processes.
(ii) In case of even number of items or continuous series, it is an estimated value other than the values in the series.
(iii) When there is a large difference in the values of items, median is not an appropriate method.
(iv) To calculate median, series needs to be arranged in ascending or descending order, which is a lengthy process.
Q.14. When is it appropriate to use inspection method to identify model value of a series?
Ans. It is appropriate to use inspection method to identify model value of a series when all the items in the series have different frequencies.
Q.15. List the different types of modal data.
Ans. The different types of modal data are:
(i) Unimodal Data – data with unique mode
(ii) Bimodal Data – data with two modes
(iii) Multimodal Data – data with more than two modes
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