# Statistics class 10 Notes Mathematics

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## CBSE Guide Statistics class 10 Notes

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## 10 Mathematics notes Chapter 14 Statistics

Download CBSE class 10th revision notes for Chapter 14 Statistics in PDF format for free. Download revision notes for Statistics class 10 Notes and score high in exams. These are the Statistics class 10 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.

CBSE Class 10 Mathematics
Revision Notes
CHAPTER 14
STATISTICS

1. Mean of Grouped Data
2. Mode of Grouped Data
3. Median of Grouped Data
4. Graphical Representation of CF
5. Miscellaneous Questions

1. Mean : The mean for grouped data can be found by :

(i) The direct method =$\bar X = \frac{{\sum {fixi} }}{{\sum {fi} }}$

(ii) The assumed mean method

$\bar X = a + \frac{{\sum {fidi} }}{{\sum {fi} }}$

Where $\begin{gathered} {d_i} = {x_i} - a. \end{gathered}$ a = Provisional mean

(iii) The step deviation method

$X = a + \frac{{\sum fiui}}{{\sum fi}}\; \times h,\;\;\;\;\;where\;\;\;{U_l} = \frac{{{X_i} - a}}{h}$

2. Mode : The mode for the grouped data can be found by using the formula :

$mode = l + \left[ {\frac{{{f_1} - {f_0}}}{{2{f_1} - {f_0} - {f_2}}}} \right]\; \times h$

$l$= lower limit of the modal class.

${f_1}$ = frequency of the modal class.

${f_o}$ = frequency of the preceding class of the modal class.

${f_2}$= frequency of the succeeding class of the modal class.

h = size of the class interval.

Modal class – class interval with highest frequency.

3. Median : Median of continuous series is:

(i) ${\left( {{{\rm{N}} \over 2}} \right)^{th}}$ term (if number of terms are odd)

(ii) ${1 \over 2}\left[ {{{\left( {{{\rm{N}} \over 2}} \right)}^{th}}{\rm{term}} + {{\left( {{{\rm{N}} \over 2} + 1} \right)}^{th}}{\rm{term}}} \right]$ (if number of terms are even]

(iii) The median for the grouped data can be found by using the formula :

$median = l + \left[ {\frac{{n/2 - Cf}}{f}} \right] \times h$

$l$= lower limit of the median class.

n = number of observations.

Cf = cumulative frequency of class interval preceding the median class.

f = frequency of median class.

h = class size.

4.Empirical Formula : Mode = 3 median – 2 mean.

5.Cumulative frequency curve or an Ogive :

(i) Ogive is the graphical representation of the cumulative frequency distribution.

(ii) Less than type Ogive :

• Construct a cumulative frequency table.

• Mark the upper class limit on the x-axis.

(iii) More than type Ogive :

• Construct a frequency table.

• Mark the lower class limit on the x-axis.

(iv) To obtain the median of frequency distribution from the graph :

• Locate point of intersection of less than type Ogive and more than type Ogive :

Draw a perpendicular from this point on x-axis.

• The point at which it cuts the x-axis gives us the median.