Mean Median Mode and Probability Formulas with Solved Examples for Class 10 Statistics
Class 10 is of the crucial classes in a student’s life as it becomes a deciding factor for their career choices. Students find them psychologically facilitated in selecting an apt stream for further studies – Commerce, PCM, PCB, or Arts. That said, maths is one of the significant subjects as it is a basic need for a lot of career choices, even for cracking competitive exams like IIT JEE, FMS, CAT, XAT or All India Services etc. even government job exams require an understanding of mathematics. However, mastering over mathematics can become like a cakewalk when you are familiar with the formulas.
Benefits of Class 10 Statistics Formulas
Since the concepts covered in class 10 mathematics and statistics period are asked in various competitive exams, like CAT, MAT, JEE and even government job exams, it becomes all the more essential to have a firm understanding of the formulas. Vedantu is providing you with the complete list of Maths formulae for Class 10 that will sufficiently help you with board exam preparation.
All Formulas of Statistics Class 10
You will find a list of statistics class 10 all formulas at the official website of Vedantu. Below is a comprehensive list of class 10 statistics formulas that you will be able to save, print and download free PDF.
The comprehensive formula sheet includes:
Mean
Mean of raw data
Mean of grouped data
Mean of discrete data
Median
Median of raw data
Median of grouped data
Median of discrete data
Mode
Mode of raw data
Mode of grouped data
Mode of discrete data
Range
Formula to calculate range = Maximum value – Minimum value
As an example, let’s take a data with values as below:
7, 45, 62, 47, 21, 98, 77, 85, 33, 31, 27, 51, 36, 58
Range = Maximum value – Minimum value
= 98 - 7
= 91
Formula For Statistics Class 10 CBSE Maths
Mean
In statistical mathematics, the mean value of a variable is described as the sum total of all the values of the variable divided by its number of values. Class 10 maths statistics mean am = a1 + a2 + a3 + a4 + a5/5 Σno/n.
Median
In statistical mathematics, the median of a data set of values is the centermost value of the data set when it has been ordered in ascending order. That is, from the lowest value to the largest value. Median is calculated using the following formula:
½ (n+1)
Where n = number of values in the data.
Given that the number of values in the set of data is even, then the median is the average of the two central values.
Mode
Mode of a statistical data is the value of that variable of a data set which consists of the maximum frequency.
Formula of Statistics Class 10 Grouped Mean
Mean: If x1, x2, x3, x4, x5, x6, x7……xn are observations with respective frequencies f1, f2, f3, f4, f5, f6, f7…..fn then mean is given as:
For Grouped Data
M.D (mean) = \[\frac{\sum f|x - \mu|}{N}\]
Formula of Statistics Class 10 Grouped Median
Median: For a given set of data, we require to have a frequency distribution, class interval, and cumulative frequency distribution. Then, the median is calculated in the below given manner:
\[Median = l + \frac{[\frac{N}{2} - m]}{f} \times c\]
In which,
l is the lower limit of median class,
N is the total number of observations,
cf is the cumulative frequency of class earlier in the median class,
f is the frequency.
h is the class size (supposing class size to be equivalent).
Formula of Statistics Class 10 Grouped Mode
Mode or the Modal class is the class interval consisting of the highest frequency. Mode is acquired using the modal class mode formula as given in the below image:
(image will be uploaded soon)
In which,
l is the lower limit of the modal class of the mode,
h is the size of the class interval (supposing all class sizes to be equivalent),
f1 is the frequency
f0 is the frequency of the class earlier to the modal class,
f2 is the frequency of the class after the modal class.
FAQs on CBSE Class 10 Maths Statistics Complete Formula Guide
1. What are the important formulas in CBSE Class 10 Maths Statistics?
The important CBSE Class 10 Maths Statistics formulas include formulas for mean, median, and mode for grouped and ungrouped data.
- Mean (Ungrouped Data) = Σx / n
- Mean (Grouped Data – Direct Method) = Σfᵢxᵢ / Σfᵢ
- Mean (Assumed Mean Method) = a + (Σfᵢdᵢ / Σfᵢ)
- Mean (Step Deviation Method) = a + (Σfᵢuᵢ / Σfᵢ) × h
- Median (Grouped Data) = l + [(n/2 − cf) / f] × h
- Mode (Grouped Data) = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
2. What is the formula for mean in statistics Class 10?
The mean formula in Class 10 Statistics is Σfᵢxᵢ / Σfᵢ for grouped data and Σx / n for ungrouped data.
- Σfᵢxᵢ = sum of (frequency × class mark)
- Σfᵢ = total frequency
3. What is the formula for median in grouped data?
The median formula for grouped data is l + [(n/2 − cf) / f] × h.
- l = lower boundary of median class
- n = total frequency
- cf = cumulative frequency before median class
- f = frequency of median class
- h = class width
4. What is the formula for mode in Class 10 Statistics?
The mode formula for grouped data is l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h.
- l = lower boundary of modal class
- f₁ = frequency of modal class
- f₀ = frequency of preceding class
- f₂ = frequency of succeeding class
- h = class size
5. How do you find the mean using the step deviation method?
The step deviation method formula is Mean = a + (Σfᵢuᵢ / Σfᵢ) × h.
- Choose a as assumed mean
- Find dᵢ = xᵢ − a
- Calculate uᵢ = dᵢ / h
- Apply the formula
6. What is cumulative frequency in statistics?
The cumulative frequency is the running total of frequencies up to a given class interval.
- Add frequencies successively from top to bottom.
- Used to find the median and draw ogives.
7. How do you find the class mark in statistics?
The class mark is the midpoint of a class interval and is calculated as (Upper limit + Lower limit) / 2.
- Example: For class 10–20
- Class mark = (10 + 20)/2 = 15
8. What is the difference between mean, median, and mode?
The mean, median, and mode are measures of central tendency but differ in definition.
- Mean: Average of all observations.
- Median: Middle value when data is arranged in order.
- Mode: Most frequently occurring value.
9. How do you find the median class in grouped data?
The median class is the class interval whose cumulative frequency first exceeds n/2.
- Step 1: Find total frequency (n).
- Step 2: Compute n/2.
- Step 3: Identify the class where cumulative frequency ≥ n/2.
10. What is the empirical relation between mean, median, and mode?
The empirical relation in statistics is Mode = 3 × Median − 2 × Mean.
- This relation is used for moderately skewed distributions.
- It helps estimate mode when mean and median are known.
