Sum

The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method.

Time (hrs.) | 0 - 2 | 2 - 4 | 4 - 6 | 6 - 8 | 8 - 10 |

No. of students | 7 | 18 | 12 | 10 | 3 |

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#### Solution

Class
(Time in hours) |
Class Mark x _{i} |
Frequency (Number of students) f _{i} |
Class mark × Frequency x _{i}f_{i } |

0 - 2 | 1 | 7 | 7 |

2 - 4 | 3 | 18 | 54 |

4 - 6 | 5 | 12 | 60 |

6 - 8 | 7 | 10 | 70 |

8 - 10 | 9 | 3 | 27 |

\[\sum_{} f_i = 50\] | \[\sum_{} x_i f_i = 218\] |

Mean = \[\frac{\sum_{} x_i f_i}{\sum_{} f_i}\]

\[= \frac{218}{50}\]

= 4.36 hours

Hence, the mean time spent by students for their studies is 4.36 hours.

Concept: Tabulation of Data

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