RBSE Class 9 Maths Notes Chapter 14 Statistics

These comprehensive RBSE Class 9 Maths Notes Chapter 14 Statistics will give a brief overview of all the concepts.

RBSE Class 9 Maths Chapter 14 Notes Statistics

1. The extraction of meaningful information from collected data is studied in a branch of mathematics called statistics.

2. In this chapter, we shall study collection of data, presentation, representation by figures, mean, median and mode of ungrouped data.

3. The facts or figures, which are numerical or otherwise, collected with a definite purpose are called data. Statistical data are of two types.
(i) Primary data
(ii) Secondary data

(i) Primary data : When an investigator collects data himself with a definite plan or design in his filer) mind, it is called primary data.

(A) Primary data are collected by the following methods :
(a) Direct Personal Investigation
(b) Indirect Investigation.

(B) Indirect investigation can be carried out in the following ways :
(a) Filling the list by enumerator
(b) Filling the list by informer
(c) By local sources or correspondent
(d) Direct oral investigation by the specialists.

(ii) Secondary data : Data which are not originally collected rather obtained from published or unpublished sources are known as secondary data.

4. Sources of published data are as follows :

• International publication –
• Government Publication
• Semi-government publication
• Local bodies like municipal corporation and gram panchayat publications.
• Publications of universities and research institutes.
• Various papers and magazines.
• Publication of research scholars.

5. Presentation of Data : If data is large, then it is written in tabular form rather than in ascending or descending order.

6. Frequency : The number of times an observation (or event) occurs in the given data, is known as the frequency of the observation. It is denoted by ‘f’.

7. Generally, variable ‘V’ is used for marks in frequency distribution.

8. Range : The difference of the highest and the lowest values in the data is called the range of the data.

9. Mid-value or class mark : The average of the values of the lower and upper class limits of any class interval is known as its mid-value or class mark. It is denoted by.

10. Graphical Representation of Data : Graphical representation of data can be done in three ways :
(i) Bar Graph
(ii) Histograms
(iii) Frequency polygon

Bar Graph : A bar graph is a pictorial representation of data in which usually bars of uniform width are drawn with equal spacing between them on one axis (say, the x-axis), depicting the variable. The values of the variable are shown on the other axis (say, the y-axis) and the heights of the bars depend on the values of the variable.

Histograms : A histogram or frequency histogram is a graphical representation of a frequency distribution in the form of rectangles with class intervals as bases and heights proportional to corresponding frequencies such that there is no gap between any two successive rectangles.

Frequency polygon : Frequency polygon is another method of representing frequency distribution graphically. The figure obtained by joining the mid-points of the upper horizontal side of each rectangle of histogram is called a frequency polygon.

11. Three measures of central tendency for ungrouped data are :

(i) Mean : The mean of a set of observations is equal to the sum of all observations divided by the total number of observations. It is denoted by \(\bar{x}\) .
Thus,  \( \bar{x}=\frac{\sum_{i=1}^{n} x_{1}}{n} \)

For ungrouped frequency distribution it is given as
\(\bar{x}=\frac{\sum_{i=1}^{n} f_{i} x_{i}}{\sum_{i=1}^{n} f_{i}}\)

(ii) Median : Median of a given number of observations is the value of the variable which divides it exactly into two equal parts. Thus, when data is written in ascending or descending order, then median of ungrouped data is calculated as under :

(a) If the number of observations (n) is odd, then median = Value of \(\left(\frac{n+1}{2}\right)^{t h}\) observations.
(b) If the number of observation (n) is even, then
\(\dot{M e d i a n}=\frac{\text { Value of }\left(\frac{n}{2}\right)^{\text {th }} \text { observation }+\text { Value of }\left(\frac{n}{2}+1\right)^{\text {th }} \text { observation }}{2}\)

(iii) Mode : The observation which occurs maximum number of times is called mode.