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**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.

Ans.

(i) Mathematical average

(ii) Positional average

Ans.

(i) Median

(ii) Mode

(iii) Partition values â€“ quartiles, deciles and percentiles

Ans.

(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.

Ans.

(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.

Ans.

Ans.

(i) Simple arithmetic mean

(ii) Weighted arithmetic mean

Ans.

Ans.

(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.

Ans.

(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.

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Ans.

(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 open-end series.

Ans.

(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.

Ans.

Ans.

(i) Uni-modal Data â€“ data with unique mode

(ii) Bi-modal Data â€“ data with two modes

(iii) Multi-modal Data â€“ data with more than two modes

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52 videos|42 docs

### Arithmetic Mean (Part - 2)

- Video | 12:41 min
### Arithmetic Mean (Part - 3)

- Video | 17:31 min
### Median and Mode (Part - 3)

- Video | 10:05 min
### Median and Mode (Part - 4)

- Video | 09:41 min
### Median and Mode (Part - 5)

- Video | 16:17 min
### Median and Mode (Part - 6)

- Video | 09:01 min

- Median and Mode (Part - 2)
- Video | 16:44 min
- Median and Mode (Part - 1)
- Video | 14:22 min