The document defines key concepts in descriptive statistics and econometrics: - Population refers to the total collection of people/items of interest, while a sample is a subset selected for analysis to make inferences about the population. - Common measures of a sample include the mean (average), mode (most frequent value), and median (middle value). The mean is calculated by summing all values and dividing by the sample size. - Variance and standard deviation are measures of how spread out the values are from the mean, with variance calculated by subtracting each value from the mean, squaring the differences, summing them, and dividing by n-1, and standard deviation taking the square root of the variance.

1. Descriptive Statistics
Econometry

2. Population: In statistics, a population is a
collection of people, items, or events about
which you want to make inferences.
Sample: A sample is a subset of people, items, or
events from a larger population that you collect
and analyze to make inferences.
Example: In elections various agencies carry out poll surveys. Assume
assembly election of a particular state; all voters of that state is
called population in terms of statistics and the people chose to carry
out the survey which represents all voters is called sample. A
representative sample is one that contains right proportions of
people of different ethic origins, ages, social classes and sexes.

3. Mean of a sample/Sample mean usually denoted by x, is the
average and is computed as sum of all the observed
outcomes from the sample divided by the total number of
events.
Where n is the sample size and the x correspond to the
observed value.
Example-> Let there be the following numbers:
23, 29,20,32,23,21,33,25
mean= 23+29+20+32+23+21+33+25 25.75
8

4.  The mode of a set of data is the number with
the highest frequency.
 In previous example 23 occurs two times and
every other number occur only once. Hence
23 is the mode.

5.  The median is the middle score.
 If we have an even number of events we take
the average of the two middles.
 The median is better for describing the
typical value.
 It is often used for income and home prices.
Example: In previous example first we will write the
numbers in order:
20,21,23,23,25,29,32,33
Median= 23+25 24
2

6.  Calculate the mean, x.
 Write a table that subtracts the mean from each observed value.
 Square each of the differences.
 Add this column.
 Divide by n -1 where n is the number of items in the
sample This is the variance.
 To get the standard deviation we take the square root of the
variance.

7.  Example: VARIANCE(S2):
173.48 24.78=25
8-1
Standard Deviation:
Sq. rt. (25) = 5
x X-25.75 (X-25.75)2
23 -2.75 7.56
29 3.25 10.56
20 -5.75 33.06
32 6.25 39.06
23 2.75 7.56
21 -4.75 22.56
33 7.25 52.56
25 -.75 0.56
TOTAL 173.48

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