Class 10

Math

All topics

Statistics

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher | Number of states/U.T. |

$15−20$ | $3$ |

$20−25$ | $8$ |

$25−30$ | $9$ |

$30−35$ | $10$ |

$35−40$ | $3$ |

$40−45$ | $0$ |

$45−50$ | $0$ |

$50−55$ | $2$ |

Mode: The class which have highest frequency.

In this case, class interval $30−35$ is the modal class.

Now,

Lower limit of modal class, $l=30,h=5,f_{1},=10,f_{0}=9,f_{2}=3$

We know that,

Mode =$l+(2f_{1}−f_{0}−f_{2}f_{1}−f_{0} )×h$$=30+(2(10)−9−310−9 )×5$

$=30+(20−121 )5$

$=30+81 ×5$

Mode $=30.625≡30.6$

for mean,

Mean, $xˉ=∑f_{i}∑f_{i}u_{i} $

$xˉ=351022.5 =29.2$

Therefore,

Most states/U.T. have a student teacher ratio of $30.6$ and on an average, the ratio is $29.2$.