Answer

Verified

410.1k+ views

**Hint:**First we have to find the sum of scores \[\left( {\text{x}} \right)\] and the frequency \[\left( {\text{f}} \right)\]as this a discrete frequency distribution. Then by using the formula, whichever is around the answer i.e., round off is the required answer.

**Formula used:**When the number of observation is odd:

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

When the number of observation is even:

First, find ${\left( {\dfrac{{\text{N}}}{2}} \right)^{th}}$ term

Then ${\left( {\dfrac{{{\text{N + 1}}}}{2}} \right)^{th}}$ term

And find the average of two values i.e., average of ${\left( {\dfrac{{\text{N}}}{2}} \right)^{th}}$term and ${\left( {\dfrac{{{\text{N + 1}}}}{2}} \right)^{th}}$ term

**Complete step-by-step solution:**

First we have to rearrange the given data as follows:

Score \[\left( {\text{x}} \right)\] | Frequency \[\left( {\text{f}} \right)\] |

$10$ | $2$ |

$15$ | $3$ |

$20$ | $5$ |

$25$ | $6$ |

$30$ | $4$ |

${\text{N = 20}}$ |

Since the number of observation is even, we need to find average of ${\left( {\dfrac{{\text{N}}}{2}} \right)^{th}}$ term and ${\left( {\dfrac{{{\text{N + 1}}}}{2}} \right)^{th}}$ term

On putting the value of N and we get,

${\left( {\dfrac{{\text{N}}}{2}} \right)^{th}} = \dfrac{{20}}{2}$

Let us divide the term and we get

$ \Rightarrow {10^{th}}$ observation

Now we have to find:

${\left( {\dfrac{{{\text{N + 1}}}}{2}} \right)^{th}} = \dfrac{{20 + 1}}{2}$

On dividing the term and we get,

$ \Rightarrow 10.5$

Taking as round value and we get,

$ \Rightarrow {11^{th}}$ Observation

Now the changed data as formed as follows:

Score \[\left( {\text{x}} \right)\] | Frequency \[\left( {\text{f}} \right)\] | \[\left( {{\text{cf}}} \right)\] |

$10$ | $2$ | $2$ |

$15$ | $3$ | $5$ |

$20$ | $5$ | $10$ |

$25$ | $6$ | $16$ |

$30$ | $4$ | $20$ |

${\text{N = 20}}$ |

So here, ${10^{th}}$ term lies in $20$ and ${11^{th}}$ term lies in $25$

So we can write it as, by using the formula and find the median

Median = $\dfrac{{20 + 25}}{2}$

Let us add the numerator and we get,

Median = $\dfrac{{45}}{2}$

Let us divide the term and we get,

Median =$22.5$

**Therefore the correct answer is ${\text{B) 22}}{\text{.5}}$.**

**Note:**In this question we have an alternative method.

Alternative method:

We can also find median in a simple way.

Score \[\left( {\text{x}} \right)\] | Frequency \[\left( {\text{f}} \right)\] |

$10$ | $2$ |

$15$ | $3$ |

$20$ | $5$ |

$25$ | $6$ |

$30$ | $4$ |

Here we can also write this elaborately since it is discrete distribution,$10,10,15,15,15,20,20,20,20,20,25,25,25,25,25,25,30,30,30,30$

Median is the middle value of the given observation, so in this observation there are two numbers in middle (since the total numbers are even)

They are $20$ and $25$

Median = average of these two numbers

Median = $\dfrac{{20 + 25}}{2}$

Let us add the numerator and we get,

Median = $\dfrac{{45}}{2}$

Let us divide the term and we get,

Median =$22.5$

Therefore the correct answer is ${\text{B) 22}}{\text{.5}}$.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

10 examples of evaporation in daily life with explanations

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell