Question

find the mean medium and mode of 6,7,8,9,14​

Answer 1

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• Find the mean, median and mode for 6,7,8,9,14.

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\textsf{Given data = 6, 7, 8, 9, 14}$

• $\boxed{\sf{Mean \: = \: \dfrac{\sum xi}{N}}}$

• $\sf{Mean \: = \: \dfrac{6\: +\: 7\: +\: 8\: +\: 9\: +\: 14}{5}}$

• $\sf{Mean \: = \: \dfrac{44}{5}}$

• $\boxed{\sf{Mean \: = \: 8.8.}}$

• $\boxed{\sf{Median \: = \: \dfrac{N \: + \: 1}{2} \: where \:n \:is \:odd.}}$

• $\sf{Median \: = \: \dfrac{5 \: + \: 1}{2}}$

• $\sf{Median \: = \: \dfrac{6}{2} \: = \: 3rd \: term.}$

• $\boxed{\sf{Median \: = \: 8.}}$

• $\boxed{\textsf{Mode = Most number of times a term is recurring.}}$

• $\boxed{\textsf{There is no mode for the given data.}}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf{Mean \: = \: 8.8.}}}$

• $\boxed{\therefore{\sf{Median \: = \: 8.}}}$

• $\boxed{\therefore{\textsf{There is no mode.}}}$

$\huge{\bf{\purple{\mathfrak{Extra \: Information:-}}}}$

• Arithmetic mean:-
• The average of the given data.
• $\sf{Mean \: = \: \dfrac{\sum xi}{N}}$
• where,
• $\sf{\sum xi}$ is the sum of the terms.
• N is the number of terms.

• Median:-
• The middle most value of the given data.
• While finding median, we have to arrange the data in ascending or descending order.
• $\sf{\dfrac{N}{2}}$ is used when N is even.
• $\sf{\dfrac{N \: + \: 1}{2}}$ is used when N is odd.

• Mode:-
• The value that recurrs most of the times in a given data.

Answer 2

${\large{\pmb{\sf{\underline{Finding \; mean \: 1^{st}}}}}}$

Procedure: To find the mean of any term we have to add all the given digits firstly then when the sum came then we have to divide it by the total number of already given terms. And then at last we get our final result as mean. Formula to find mean is given below, we have to use it too. Let's solve this question!

${\small{\underline{\boxed{\sf{\rightarrow \dfrac{Sum \: of \: terms \: or \: observations}{Total \: number \: of \: terms \: or \: observations}}}}}}$

${\sf{\mapsto Total \: number \: of \: observations \: = 5}}$

${\sf{\mapsto Observations \: are \: 6,7,8,9 \: and \: 14}}$

By using the formula to find mean let us solve this question!

${\sf{\mapsto \dfrac{Sum \: of \: terms \: or \: observations}{Total \: number \: of \: terms \: or \: observations}}}$

${\sf{\mapsto \dfrac{6+7+8+9+14}{5}}}$

${\sf{\mapsto \dfrac{13+8+9+14}{5}}}$

${\sf{\mapsto \dfrac{21+9+14}{5}}}$

${\sf{\mapsto \dfrac{30+14}{5}}}$

${\sf{\mapsto \dfrac{44}{5}}}$

${\sf{\mapsto 8.8}}$

${\pmb{\frak{\underline{\therefore 8.8 \: is \: the \: mean}}}}$

${\large{\pmb{\sf{\underline{Finding \; median \: 2^{nd}}}}}}$

Procedure: To find median firstly we have to make the terms in ascending or descending order as we want. Then we have to check the middle term there. Then we get our answer means middle terms in that sequence is the median but if there is no middle term coming means for example there are total 6 terms then it obvious that in middle no term will come because it be even then we have to add two middle terms then we have to divide it by two. Ascending order? Small number to big number. And we get our final result! Let's solve this.

${\sf{\mapsto Observations \: are \: 6,7,8,9 \: and \: 14}}$

${\sf{\mapsto Total \: number \: of \: observations \: = 5}}$

${\sf{\mapsto Ascending \: order \: = 6,7,8,9,14}}$

${\sf{\mapsto The \: middle \: term \: is \: 8}}$

${\pmb{\frak{\underline{\therefore 8 \: is \: the \: median}}}}$

${\large{\pmb{\sf{\underline{Finding \; mode \: 3^{rd}}}}}}$

Procedure: To find mode we have to check that which number came more time. And according to the question there are no mode because all numbers are just coming for a time.

${\sf{\mapsto Observations \: are \: 6,7,8,9 \: and \: 14}}$

${\sf{\mapsto All \: numbers \: are \: coming \: for \: just \: a \: time}}$

${\pmb{\frak{\underline{\therefore No \: observation \: is \: the \: mode}}}}$