Sindh Text New Math Book solve Class 10th unit 22. definitions and ex#22.1 solved.
Sindh Text New Math Book solve Class 10th unit 22. definitions and ex#22.1 solved.
Unit 22: BASIC STATISTICS
STATISTICS
Statics is a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data.
UNGROUPED DATA
When the data has not been placed in any categories and no cation/summarization has taken place on the data then it is known as grouped data. Ungrouped data is also known as raw data.
GROUPED DATA
When raw data have been grouped in different classes then it is said to
be grouped data
QUALITATIVE DATA
Qualitative data are measurements for which there is no natural scale, but which consist of attributes, labels, or other non-numerical characteristics.
QUANTITATIVE DATA
Quantitative data are numerical measurements that arise from a natural numerical scale.
DISCRETE DATA
Discrete data is a count that involves integers - only a limited number of values is possible. This type of data cannot be subdivided into different arts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers. In many cases, discrete data can be prefixed with "the number of".
For example:
1. The number of students who have attended the class;
2. The number of customers who have bought different products;
CONTINUOUS DATA
Continuous data is considered the complete opposite of discrete data. It's the type of numerical data that refers to the unspecified number of possible measurements between two presumed points.
The numbers of continuous data are not always clean and integers, as they are usually collected from very precise measurements. Measuring a particular subject is allowing for creating a defined range to collect more data.
Variables in continuous data sets often carry decimal points, with the number stretching out as far as possible. Typically, it changes over time.
It can have completely different values at different time intervals, which might not always be whole numbers. Here are some examples:
1. The weather temperature
2. The wind speed
3. The weight of the kid's
PARAMETER
A parameter is a number that summarizes some aspect of the population as a whole. A statistic is a number computed from the sample data.
POPULATION
A population is any specific collection of objects of interest.
SAMPLE
A sample is any subset or sub-collection of the population, including cases where the sample consists of the whole population, which case is termed a census.
FREQUENCY DISTRIBUTION:
A frequency distribution is a tabular description of grouped data. consisting of classes and corresponding frequencies.
FREQUENCY
Frequency is basically the number of times a data item occurs in the series. In other words, it deals with how frequent a data item is in the series.
For example, if the weight of 5 students in a class is exactly 65 kg, then the frequency of data item 65kg is 5.
RANGE:
The range is the difference between the highest and lowest observations in the given data. i.e.
Range = [Highest observation] - [Lowest observation]
CLASS LIMITS
These are numbers used to identify a class. For each class, there is the smallest number called lower class lint (LCL), and the largest number called upper-class limit (UCL). The observations starting from the LCL u to the UCL fall in a particular class.
CLASS INTERVAL/WIDTH(H):
The class interval can be defined as the size or length of the class, and compute y finding difference between any two consecutive LCLs or UCLS. We usually use constant clas width or interval, denoted by h.
Where K is the number of classes, R is the range and m is the number of maxi decimal places in the observations.
If data are disa one decimal place discrete, then m = 0, if data are continuous with values up to al places, then m= 1 and so on. For example
4 m = 0 , 4.2 m = 1 , 4.23 m = 2
NUMBER OF CLASS {K}.
The number of classes is denoted by K and it ranges from 5 to 15 depending on the number of observations and range.
H STURGES RULE
H Sturges (1926) suggested a rule to calculate a desirable number of K by using the number of observations n.
The Sturges' rule is H. Sturges by defined as:
K = [1 +3.322log(n)]
where log(n) is the logarithm of n with base 10, and 11 is ceiling approximation.
SPACING BETWEEN THE CLASSES(d):
The constant difference between the Lower class limit of a class and the Upper-Class limit of the next class is known as spacing between the classes. If m is a number of maximum decimal digits then:
, m = 0,1,2,.....
CLASS BOUNDARIES:
The numbers which separate a class from adjoining classes are called class boundaries. Class boundaries can be determined by the following formulas:
CLASSMARKS/MIDPOINT:
The arithmetic mean of the class limits or class boundaries in grouped data with continuous classes is known as Class marks or midpoints.
Classmark or midpoint can be determined by the following formulas:
CUMULATIVE FREQUENCY
The cumulative frequency is the total of frequencies, in which the frequency of the first class interval is added to the frequency of the Second class interval and then the sum is added to the frequency of the third class interval, and so on.
CENTRAL TENDENCY
The ability of all observations in data to cluster around a central point is referred to as the central tendency. A central point of the data is called the measure of central tendency.
ARITHMETIC MEAN:
Also known as the arithmetic average. It is calculated by the summation of all values divided by the number of values.
GEOMETRIC MEAN
A geometric mean is a mean or average which shows the central ten of a set of numbers by using the product of their values.
HARMONIC MEAN
A simple way to define a harmonic mean is to call it the reciprocal arithmetic mean of the reciprocals of the observations. The important criterion for it is that none of the observations should be zero.
Ungroup data.
MEDIAN:
The median of a dataset is described as the middlemost value in the ordered arrangement of the values in the dataset.
MODE:
The most frequently occurring item/value in a data set is called mode Bimodal is used in the case when there is a tie b/w two values. Multimodal is when a given dataset has more than two values with the same occurring frequency.
PERCENTILE:
This form of central tendency divides a group of data into 100 parts. The nth percentile of a dataset is described as n values below that “nth value" and (100-n) values above that “nth value”.
QUARTILE:
This form of central tendency divides a group into four subparts.
First Quartile =25th percentile
Second Quartile =50th percentile
Third Quartile = 75th percentile
Fourth Quartile = 100th percentile.
RANGE:
The difference b/w the largest value and the smallest value in a dataset is called the range of the data set. The range is also a representation of the end/extreme values.
Range=Max Value-Minimum Value.
VARIANCE:
It is the square of deviations about the arithmetic mean for set numbers.
STANDARD DEVIATION.
It is the square root of variance.
Click on the download button and download exercise 22.1 completely solved.
