Question

class 10 maths

statics

baas

easy mei explain ​

Answer 1

Introduction of Statistics: Statistics is the study of collection, analysis, interpretation, and organization of data. In applying statistics too, e.g., a scientific, industrial, or societal problem, it is conventional, to begin with, a statistical population or a statistical model process to be studied. Populations can be diverse topics such as “all persons living in a country” or “every atom composing a crystal”. Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.

Mean, median and mode are three measures of central tendency. The mean of the grouped data is calculated by using the following methods: (a) Direct method (b) Assumed mean method (c) Step deviation method. The mode is that value of the observation which occurs most frequently.

If data has more than one value of the same maximum frequency, it is said to be multimodal. In a grouped frequency distribution, the class with maximum frequency is called modal class.

For example:

The mode is the value inside the modal class and is calculated by using the following formula. Mode = l + {(f1–f0) / (2f1-f0-f2) }h,

where l = lower limit of the modal class,

h = size of the class interval (assuming all class sizes to be equal),

f1 = frequency of the modal class,

f0 = frequency of the class preceding the modal class,

f2 = frequency of the class succeeding in the modal class.

Median is the value of the middle-most observation in the data. To find the median of a grouped data, first find the median class and then use the following formula:

Median = l + h {(n/2–cf)/f},

where l = lower limit of the median class

n = number of observations

cf = cumulative frequency of class preceding the median class

f = frequency of the median class

h = class size

The empirical relationship of the median with the other two measures of central tendencies can be written as: 3 Median = Mode + 2 Mean.

The cumulative frequency of a class can be obtained by adding the frequencies of all the classes preceding the given class.

Cumulative frequency distributions can be represented graphically by a cumulative frequency curve (also known as ogive). There are two types of ogives namely ‘less than’ ogive and ‘more than’ ogive.

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