Question

50 points!!!
Someone help pls, I can’t understand it and it’s due tomorrow :c

Answer 1

`{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}`

`\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}`

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

`\star \: \sf Median_((when \: n \: is \: even)) = {\underline{\boxed{\sf{\purple{ \frac{ { \bigg ((n)/(2) \bigg)}^(th)term +{ \bigg( (n)/(2) + 1 \bigg)}^(th) term } {2} }}}}}`

`\\`

`\sf Median_((when \: n \: is \: even)) ={ \frac{ { \bigg ((6)/(2) \bigg)}^(th)term +{ \bigg( (6)/(2) + 1 \bigg)}^(th) term } {2} }`

`\\`

`\sf Median_((when \: n \: is \: even)) ={ \frac{ {3}^(rd) term +{ \bigg( (6 + 2)/(2) \bigg)}^(th) term } {2} }`

`\\`

`\sf Median_((when \: n \: is \: even)) ={ \frac{ {3}^(rd) term +{ \bigg( \cancel{ (8)/(2)} \bigg)}^(th) term } {2} }`

`\\`

`\sf Median_((when \: n \: is \: even)) ={ \frac{ {3}^(rd) term +{ 4}^(th) term } {2} }`

• Putting,

3rd term as 4 and the 4th term as 7.

`\longrightarrow \: \sf Median_((when \: n \: is \: even)) ={ \frac{ 4 + 7 } {2} }`

`\longrightarrow \: \sf Median_((when \: n \: is \: even)) ={ \frac{ 11} {2} }`

`\longrightarrow \: \sf Median_((when \: n \: is \: even)) = \purple{5.5}`

`\\`

`{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}`

`\star\:{\underline{\underline{\sf{\red{Solution:}}}}}`

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

`\star \: \sf Median_((when \: n \: is \: odd)) = {\underline{\boxed{\sf{\red{ { \bigg( (n + 1)/(2) \bigg)}^(th) term}}}}}`

`\\`

`\sf Median_((when \: n \: is \: odd)) = {{ \bigg(\frac{ 7 + 1 } {2} \bigg) }}^(th) term`

`\\`

`\sf Median_((when \: n \: is \: odd)) = { \bigg(\cancel{(8)/(2)} \bigg)}^(th) term`

`\\`

`\sf Median_((when \: n \: is \: odd)) ={ 4}^(th) term`

• Putting,

4th term as 4.

`\longrightarrow \: \sf Median_((when \: n \: is \: odd)) = \red{ 4}`

`\\`

`{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}`

`\star\:{\underline{\underline{\sf{\green{Solution:}}}}}`

The frequency distribution table for calculations of mean :

☆ Calculating the
`\sum f_(i)`

`\implies 4 + 6 + 2 + 2 + 1 + 1`

`\implies 16`

☆ Calculating the
`\sum f_(i)x_(i)`

`\implies 12 + 6 + 14 + 8 + 6 + 2`

`\implies 48`

As we know,

Mean by direct method :

`\: \: \boxed{\green{{ { \overline{x} \: = \sf ( \sum \: f_(i)x_(i))/( \sum \: f_(i))}}}}`

here,

•
`\sum f_(i)` = 16

•
`\sum f_(i)x_(i)` = 48

By putting the values we get,

`\sf \longrightarrow \overline{x} \: = \: (48)/(16)`

`\sf \longrightarrow \overline{x} \: = \green{3}`

`{\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}`

• Swipe to see the full answer.

`\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}`