- Flash back from IX Class
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- Mean for Ungroup Frequency table
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- Mean for group Frequency table
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- Various ways to calculate mean
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- Mode for grouped frequency table
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- Cumulative Frequency chart
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- Median of a grouped data frequency table
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- Empirical Formula between Mode, Mean and Median

- Statistics deals with collection, presentation, analysis and interpretation of numerical data.
- Arranging data in a 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**

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

Mark obtained(x_{i}) |
25 |
35 |
45 |
65 |

No of student(f_{i)} |
4 |
10 |
23 |
34 |

Class interval |
10-25 |
25-45 |
45-65 |
65-85 |

No of student(f_{i)} |
4 |
10 |
23 |
34 |

Where

a=> Assumed mean

d

Where

a=> Assumed mean

u

Where

l = lower limit of the modal class,

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

f

f

f

Class interval ( Age) |
No of Insurance policies |

15-20 |
2 |

20-25 |
4 |

25-30 |
16 |

30-35 |
20 |

35-40 |
20 |

40-45 |
12 |

Age in years |
Cumulative No of Insurance policies |

Less than 20 years |
2 |

Less than 25 years |
6 |

Less than 30 years |
22 |

Less than 35 years |
42 |

Less than 40 years |
62 |

Less than 45 years |
74 |

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)

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