Q1. What are the characteristics of a good measure of central tendency? [5Marks](b) What are the uses of averages? [5 Marks]Answer:a). The characteristics of a good measure of central tendency are: Present mass data in a concise form
The mass data is condensed to make the data readable and to use it for further analysis.• Facilitate comparison
It is difficult to compare two different sets of mass data. But we can compare those twoafter computing the averages of individual data sets.While comparing, the same measure of average should be used. It leads to incorrectconclusions when the mean salary of employees is compared with the median salary of the employees.• Establish relationship between data sets
The average can be used to draw inferences about the unknown relationships betweenthe data sets. Computing the averages of the data sets is helpful for estimating theaverage of population.• Provide basis for decision-making
In many fields, such as business, finance, insurance and other sectors, managerscompute the averages and draw useful inferences or conclusions for taking effectivedecisions.The following are the requisites of a measure of central tendency:•It should be simple to calculate and easy to understand•It should be based on all values•It should not be affected by extreme values•It should not be affected by sampling fluctuation•It should be rigidly defined•It should be capable of further algebraic treatment
b) Appropriate Situations for the use of Various Averages
1. Arithmetic mean is used when:a. In depth study of the variable is neededb. The variable is continuous and additive in naturec. The data are in the interval or ratio scaled. When the distribution is symmetrical2. Median is used when:a. The variable is discreteb. There exists abnormal valuesc. The distribution is skewedd. The extreme values are missinge. The characteristics studied are qualitativef. The data are on the ordinal scale3. Mode is used when:a. The variable is discreteb. There exists abnormal valuesc. The distribution is skewedd. The extreme values are missinge. The characteristics studied are qualitative4. Geometric mean is used when:a. The rate of growth, ratios and percentages are to be studiedb. The variable is of multiplicative nature5. Harmonic mean is used when:a. The study is related to speed, timeb. Average of rates which produce equal effects has to be found
(1) Plural Sense:
In plural sense, the word statistics refer to numerical facts and figures collected in a systematic manner with a definite purpose in any field of study. In this sense, statistics are also aggregates of facts which are expressed in numerical form. For example, Statistics on industrial production, statistics or population growth of a country in different years etc.
(3) Plural of Word “Statistic”:
The word statistics is used as the plural of the word “Statistic” which refers to a numerical quantity like mean, median, variance etc…, calculated from sample value.
Quota sampling is a non-probability sampling technique wherein the assembled sample has the same proportions of individuals as the entire population with respect to known characteristics, traits or focused phenomenon. by Joan Joseph Castillo (2009)
In addition to this, the researcher must make sure that the composition of the final sample to be used in the study meets the research’s quota criteria. EXAMPLE OF QUOTA SAMPLES
In a study wherein the researcher likes to compare the academic performance of the different high school class levels, its relationship with gender and socioeconomic status, the researcher first identifies the subgroups. Usually, the subgroups are the characteristics or variables of the study. The researcher divides the entire population into class levels, intersected with gender and socioeconomic status. Then, he takes note of the proportions of these subgroups in the entire population and then samples each subgroup accordingly. WHEN...
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