Download Statistics: Understanding Frequency Distributions, Moments, and Measures of Dispersion and more Exercises Statistics in PDF only on Docsity!
Question:
what is meant by marginal probability function?.
Answer:
The individual probability function of t
he random variables,from the joint probability function,is known as marginal probability
function.
Question:
In which distributions we used empirical rule & chebychev rule?.
Answer:
Empirical rule is applicable to the mound- shape, symmetrical and unim
odle (bell shaped)distributions while chebychev apply to any
distribution regardless of the shape of the frequency distribution of the data.
Question:
What is the difference between frequency and frequency distribution.?
Answer:
Frequency: The number of observations falling in a particular class is known as class frequency or simply frequency. Frequency distribution. When we arrange the frequencies in a form of table then it is known as Frequency distribution.
Question:
What is the difference between permutation and combination.
Answer:
Permutations: When
our
purpose
is
to
arrange
the
objects
with
respect
to
order
out
of"
n"
then
we
use
permutations.
Combinations: When
we
select
our
objects
out
of
"n"
with
out
considering
order
then
we
apply
combination.
Question:
What is the difference between cumulative frequency distribution and Cumulative Frequency Polygon?.
Answer:
There is no difference between cumulative frequency distribution & Cumulative Frequency Polygon,because the graph of cummulative frequency distrbution is known as Cumulative Frequency Polygon/ogive.
Question:
What is the relation between these two Moments & Moment Ratios.?
Answer:
Moments: A moment designates the power to which deviations are raised before averaging the
m. Moment ratio: These are certain
ratios in which both numerators and the denominators are moments.
Question:
What is meant by mid-rang and mid-quartile range and what is the difference between these two ranges.?
Answer:
MID-RANGE: If there are n observations with x0 and xm as their smallest and largest observations respectively, then their mid-range is defined as Mid range=X0+Xm/2. It is obvious that if we add the smallest value with the largest, and divide by 2, we
will get
a value which is more or less in the middle of the data-set. MID-
QUARTILE RANGE: If x1, x2… xn are n observations with
Q1andQ3 as their first and third quartiles respectively, then their mid-
quartile range is defined as Mid Quartile range= Q1+Q3 /2.
Difference: They both used as me
asures of central tendency because they both provide us with more or less the middle value of data.
The difference is that the mid-
quartile range is an attempt to address the problem of the range being heavily dependent on extreme
scores. An mid-quartile range represents the middle 50% of the scores in the distribution.
Question:
What is Mean, Median & Mode?
Answer:
Mean: The arithmetic mean is the statistician’s term for what the layman knows as the average. The arithmetic mean or simply the mean is a value obtained by dividing the sum of all the observations by their number. THE MEDIAN: The median is the middle value of the series when the variable values are placed in order of magnitude. THE MODE: The mode is defined as that value which occurs most frequently in a set of data i.e. it indicates the most common result. The median indicates the middle position while the mode provides information about the most frequent value in the distributio n or the set of data.^ Both median & mode are differ ent methods of calculating the average value of data and they have their advantages & disadvantages .They are used by the statisticians according to their requirement.
Question:
What is meant by Dispersion?
Answer:
Dispersion means the extent to which the data/values are spread out from the average. Example: There are many situations in which two different data having the same average e.g. Data 1:5, 5,5,5,5 having mean=5 Data 2:1, 5,6,6,7 having mean=5 Hence in such a situation we, need a measure whi
ch tell us how dispersed the data are. The measure used for this purpose is
called measure of dispersion.
Question:
What is meant by Statistics? What are its Branches ,restrictions & uses?
Answer:
MEANING OF STATISTICS:
The word “Statistics” which comes from the Latin words status , meaning political state, originally meant information useful to the state. In the first place, the word statistics refers to “numerical facts systematically arranged
- Determine the RANGE (difference between the smallest &largest values in data) data. 3. Decide where to locate the class limit (numbers typically use to identify the classes). 4. Determine the reaming class limits by adding the class interval repeatedly. 5. Distribute the data into classes by using tally marks and sum it in frequency column. Finally, total the frequency column to see that all data have been accounted for.
Question:
What is Box & Whisker Plot?
Answer:
B
ox and Whisker Plot (or Box plot): A box and whisker plot is a way of summarizing a set of data measured on an interval scale. It is often used in exploratory d ata analysis. It is a type of graph which is used to show the shape of the distribution, its cen tral value, and variability. The picture produced consists of the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median. A box plot (as it is often called) is especially helpful for indicating wheth er a distribution is skewed and whether there are any unusual observations (outliers) in the data set. Box and whisker plots are also very useful when large numbers of observations are involved and when two or more data sets are being compared.
Question:
What is Skewness?
Answer:
Skewness is defined as asymmetry in the distribution of the sample data values. Values on one side of the distribution tend t o be further from the 'middle' than values on the other side. For skewed data, the usual measures of location will give different values, for example, mode<median<mean would indicate positive (or right) skewness. Positive (or right) skewness is more common than negative (or left) skewness. If there is evidence of skewness in the data, we can apply transformations, for example, taking logarithms of positive skew data.
Question:
What is population?
Answer:
A population is any entire collection of people, animals, plants or things from which we may collect data. It is the entire g roup we are interested in, which we wish to describe or draw conclusions about. In order to make any generalizations about a population, a sample, that is meant to be representative of the population, is o ften studied. For each population there are many possible samples. A sample statistic gives information about a corresponding population parameter. For example, the sample mean for a set of data would give information about the overall population mean. It is important that the investigator carefully and completely defines the pop ulation before collecting the sample, including a description of the members to be included. Example: The population for a study of infant health might be all children born in the Pakistan in the 1980's. The sample might be all babies born on 7th May in any of the years
Question:
What is a Sample?
Answer:
A sample is a group of units selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions about the
larger group. A sample is generally selected for study because the population is too large to study in its entirety. The sample should be representative of the general population. This is often best achieved by random sampling. Also, before collecting the sample, it is important that the researcher carefully and completely defines the population, including a description of the members to be included. Example: The population for a study of infant health might be all children born in the Pakistan in the 1980's. The sample might be all babies born on 7t h May in any of the years.
Question:
What is Statistic?
Answer:
A statistic is a quantity that is calculated from a sample of data. It is used to give information about unknown values in th e corresponding population. For example, the average of the da ta in a sample is used to give information about the overall average in the population from which that sample was drawn. It is possible to draw more than one sample from the same population and the value of a statistic will in general vary from sample to s ample. For example, the average value in a sample is a statistic. The average values in more than one sample, drawn from the same popula tion, will not necessarily be equal. Statistics are often assigned Roman letters (e.g. m and s), whereas the equivalent unknown values in the population (parameters ) are assigned Greek letters (e.g. μ )
Question:
What are the different ways of representing the frequency distribution graphically?
Answer:
There are three ways of graphical representation of frequency distribution. HISTOGRAM: A histogram consists of a set of adjacent rectangles whose bases are marked off by class boundaries along the X- axis, and whose heights are proportional to the frequencies associated with the respective classes. FREQUENCY POLYGON: A frequency polygon is obtained by plotting the class frequencies against the mid- points of the classes, and connecting the points so obtained by straight line segments. FREQUENCY CURVE: When the frequency polygon c onstructed over class intervals made sufficiently small for a large number observation, is smoothed, it approaches a continuous curve, such a curve is called Frequency Curve. Types of Frequency Curves: The frequency distribution occurring in practice, usually belong to one of the following four types. You will study about them in your next lecture.
The Symmetrical Distribution.
Moderately Skewed Distribution.
Extremely Skewed or J-shaped Distribution
U-Shaped Distribution http://www.vustudents.net
Question:
What is meant by 5-Number Summary?
Answer:
Number Summary: A 5-number summary is especially useful when we have so many data that it is sufficient to present a summary of the data rather t han
