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Height(in cm) | 160 | 150 | 152 | 161 | 156 | 154 | 155 |

Number of students | 12 | 8 | 4 | 4 | 3 | 3 | 7 |

Find the median of distribution-

A)154 B)155 C)160 D)161

Answer
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Median distribution= ${\dfrac{{\text{n}}}{2}^{{\text{th}}}}{\text{term}}$ where n is total frequency.

If n is odd number use the formula,

Median distribution=${\dfrac{{\left( {{\text{n + 1}}} \right)}}{2}^{{\text{th}}}}{\text{term}}$ where n is total frequency. Find the term.

Here, we are given the height of students and number of students. First we will arrange the heights in ascending order and find the cumulative frequency. For this we will make three tables instead of two and calculate the data in the following manner- as $150$ is the smallest number here,it will come first then we will go in ascending order upto $161$.

Height(in cm) | Frequency | Cumulative frequency |

150 | 8 | 8 |

152 | 4 | 8 + 4 = 12 |

154 | 3 | 12 + 3 = 15 |

155 | 7 | 15 + 7 = 22 |

156 | 3 | 22 + 3 = 25 |

160 | 12 | 25 + 12 = 37 |

161 | 4 | 37 + 4 = 41 |

If the total frequency is even number use formula-

Median distribution= ${\dfrac{{\text{n}}}{2}^{{\text{th}}}}{\text{term}}$ where n is total frequency. If n is odd number use the formula,

Median distribution=${\dfrac{{\left( {{\text{n + 1}}} \right)}}{2}^{{\text{th}}}}{\text{term}}$ where n is total frequency.

Since here, the total number of students is $41$ which is an odd number. So we will use the formula-

$ \Rightarrow $ Median distribution=${\dfrac{{\left( {{\text{n + 1}}} \right)}}{2}^{{\text{th}}}}{\text{term}}$ where n is total frequency. Here n is the total number of students. So on putting the values, we get-

$ \Rightarrow $ Median distribution=${\dfrac{{\left( {{\text{41 + 1}}} \right)}}{2}^{{\text{th}}}}{\text{term}}$

On solving and simplifying, we get-

$ \Rightarrow $ Median distribution=${\dfrac{{\left( {{\text{42}}} \right)}}{2}^{{\text{th}}}}{\text{term = 2}}{{\text{1}}^{{\text{th}}}}{\text{term}}$

Here, we have to find the ${21^{{\text{th}}}}{\text{term}}$. So the corresponding term is $155$ as it is between ${15^{{\text{th}}}}{\text{ and }}{22^{{\text{th}}}}{\text{term}}$ .