# Ex.14.4 Q1 STATISTICS Solution - NCERT Maths Class 10

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## Question

The following distribution gives the daily income of \(50\) workers of a factory.

Daily income (in Rs) |
\(100 - 120\) | \(120 - 140\) | \(140 - 160\) | \(160 – 180\) | \(180 - 200\) |

Number of workers |
\(12\) | \(14\) | \(8\) | \(6\) | \(10\) |

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

## Text Solution

**What is known?**

The daily income of \(50\) workers of a factory.

**What is unknown?**

The less than type cumulative frequency distribution and its ogive.

**Reasoning:**

The representation of cumulative frequency distribution graphically is known as a cumulative frequency curve, or an ogive.

**Steps**:

The frequency distribution table of less than type is as follows:

Daily income (in Rs) (Upper class Limits) |
Cumulative Frequency |

Less than \(120\) | \(12\) |

Less than \(140\) | \(12 + 14 = 26\) |

Less than \(160\) | \(26 + 8 = 34\) |

Less than \(180\) | \(34 + 6 = 40\) |

Less than \(200\) | \(40 + 10 = 50\) |

Taking upper class limits of class intervals on *\(x\)*-axis and their respective frequencies on *\(y\)*-axis, its ogive can be drawn as follows: