#### Topics

##### Sets and Relations

##### Functions

##### Complex Numbers 33

##### Sequences and Series

##### Locus and Straight Line

##### Determinants

##### Limits

##### Continuity

##### Differentiation

##### Partition Values

##### Measures of Dispersion

##### Skewness

##### Bivariate Frequency Distribution and Chi Square Statistic

##### Correlation

##### Permutations and Combinations

- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Combination
- Properties of Combinations

##### Probability

##### Linear Inequations

##### Commercial Mathematics

#### description

- Variance and Standard Deviation for raw data:

- Variance and Standard Deviation for ungrouped frequency distribution:

- Variance and Standard Deviation for grouped frequency distribution :

#### notes

Let `x_1, x_2, x_3, ..., x_n` be n observations and x be their mean. Then

`(x_1 - bar x)^ 2 + (x_2 - bar x) ^2 + ... + (x_n - bar x)^ 2 `

If this sum is zero, then each `(x_i - bar x)`has to be zero. This implies that there is no dispersion at all as all observations are equal to the mean `bar x` .

If \[\displaystyle\sum_{i=1}^{n} (x_i - \bar{x})^2\] is small , this indicates that the observations `x_1, x_2, x_3,...,x_n` are close to the mean x and therefore, there is a lower degree of dispersion. On the contrary, if this sum is large, there is a higher degree of dispersion of the observations from the mean `bar x` .

#### Related QuestionsVIEW ALL [10]

Obtain standard deviation for the following date:

Height (in inches) |
60 – 62 | 62 – 64 | 64 – 66 | 66 – 68 | 68 – 70 |

Number of students |
4 | 30 | 45 | 15 | 6 |

The following distribution was obtained change of origin and scale of variable X.

d_{i} |
– 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |

f_{i} |
4 | 8 | 14 | 18 | 20 | 14 | 10 | 6 | 6 |

If it is given that mean and variance are 59.5 and 413 respectively, determine actual class intervals.

Compute variance and standard deviation for the following data:

x |
2 | 4 | 6 | 8 | 10 |

f |
5 | 4 | 3 | 2 | 1 |

Compute the variance and S.D.

x |
1 | 3 | 5 | 7 | 9 |

Frequency |
5 | 10 | 20 | 10 | 5 |

Following data gives age of 100 students in a school. Calculate variance and S.D.

Age (In years) |
10 | 11 | 12 | 13 | 14 |

No. of students |
10 | 20 | 40 | 20 | 10 |