NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Statistics

Statistics
S. noTermDescription
1StatisticsStatistics is a broad mathematical discipline which studies ways to collect, summarize, and draw conclusions from data
2DataA systematic record of facts or different values of a quantity are called data.

Data is of two types - Primary data and Secondary data.

Primary Data: The data collected by a researcher with a specific purpose in mind is called primary data.

Secondary Data: The data gathered from a source where it already exists is called secondary data

3Features of dataStatistics deals with collection, presentation, analysis, and interpretation of numerical data.

Arranging data in an order to study their salient features is called presentation of data.

Data arranged in ascending or descending order is called arrayed data or an array

Range of the data is the difference between the maximum and the minimum values of the observations

Table that shows the frequency of different values in the given data is called a frequency distribution table

A frequency distribution table that shows the frequency of each individual value in the given data is called an ungrouped frequency distribution table.

A table that shows the frequency of groups of values in the given data is called a grouped frequency distribution table

The groupings used to group the values in given data are called classes or class intervals. The number of values that each class contains is called the class size or class width. The lower value in a class is called the lower class limit. The higher value in a class is called the upper class limit.

Class mark of a class is the mid-value of the two limits of that class.

A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.

A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution

4Bar graphA bar graph is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them on one axis, usually the x-axis. The value of the variable is shown on the other axis that is the y-axis.
A Bar Graph
5HistogramA histogram is a set of adjacent rectangles whose areas are proportional to the frequencies of a given continuous frequency distribution
A Histogram
6MeanThe mean value of a variable is defined as the sum of all the values of the variable divided by the number of values.

7MedianThe median of a set of data values is the middle value of the data set when it has been arranged in ascending order. That is, from the smallest value to the highest value Median is calculated as

Where n is the number of values in the data

If the number of values in the data set is even, then the median is the average of the two middle values.

8ModeMode of a statistical data is the value of that variable which has the maximum frequency
S. No Term Description
S. noTermDescription
1Mean for Ungroup Frequency tableMean is given by

2Mean for group Frequency tableIn these distribution, it is assumed that frequency of each class interval is centered around its mid-point i.e.. class marks

Class mark

Mean can be calculated using three method

(a) Direct method

(b) Assumed mean method

Where

Assumed mean

(c) Step deviation Method

Where

a = Assumed mean

3Mode for frequency tableModal class: The class interval having highest frequency is called the modal class and Mode is obtained using the modal

grouped class

Where

I = lower limit of the modal class,

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

= frequency of the modal class,

= frequency of the class preceding the modal class,

= frequency of the class succeeding the modal class.

4Median of a grouped data frequency tableFor the given data, we need to have class interval, frequency distribution and cumulative frequency distribution

Median is calculated as

Where

l = lower limit of median class,

n = number of observations,

cf = cumulative frequency of class preceding the median class,

f = frequency of median class,

h = class size (assuming class size to be equal)

5Empirical Formula between Mode, Mean and Median3 Median = Mode + 2 Mean