☘️AnSweR:-

x = 24 and y = 21

Step-by-step explanation:

We have,

x - z = 3         ....(1) and

x + z = 45    .... (2)

To find, the values of x and y =  

Adding equations (1) and (2), we get

⇒ 2x = 48

[tex]⇒ x =

\dfrac{48}{2}[/tex]

⇒ x = 24

Put x = 24 in equation (1), we get

24 - z = 3

⇒ z = 24- 3 = 21  

∴ x = 24 and y = 21

Verified answer

Answer:

[tex]\qquad\qquad\qquad\boxed{ \bf{ \:(d) \: \: 23 \: \: }} \\ \\ [/tex]

Step-by-step explanation:

Given that,

[tex]\sf \: \overline{x} - Z = 3 - - - (1) \\ \\ [/tex]

and

[tex]\sf \: \overline{x} + Z = 45 - - - (2) \\ \\ [/tex]

On adding equation (1) and (2), we get

[tex]\sf \:2 \overline{x} = 48 \\ \\ [/tex]

[tex]\sf\implies \: \overline{x} = 24 - - - (3) \\ \\ [/tex]

On substituting the value from equation (3) in equation (2), we get

[tex]\sf \: 24 + Z = 45 \\ \\ [/tex]

[tex]\sf \: Z = 45 - 24 \\ \\ [/tex]

[tex]\sf\implies \: Z = 21 \\ \\ [/tex]

Now, We know, Median (M), Mode (Z) and Mean [tex]\overline{x} [/tex] are connected by the relationship,

[tex]\sf \: Z = 3M - 2\overline{x} \\ \\ [/tex]

On substituting the values, we get

[tex]\sf \: 21 = 3M - 2 \times 24 \\ \\ [/tex]

[tex]\sf \: 21 = 3M - 48 \\ \\ [/tex]

[tex]\sf \: 21 + 48 = 3M \\ \\ [/tex]

[tex]\sf \: 3M = 69 \\ \\ [/tex]

[tex]\sf\implies \: M = 23 \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

1. Mode of the continuous series is given by

[tex] \red{\boxed{ \boxed{\sf{Mode = l + \bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h }}}} \\ \\ [/tex]

where,

l is lower limit of modal class.

[tex] \sf{f_1} [/tex] is frequency of modal class

[tex] \sf{f_0} [/tex] is frequency of class preceding modal class

[tex] \sf{f_2} [/tex] is frequency of class succeeding modal class

h is class height

2. Mean using Direct Method

[tex]\boxed{ \rm{ \:Mean = \dfrac{ \sum f_i x_i}{ \sum f_i} \: }} \\ \\ [/tex]

3. Mean using Short Cut Method

[tex]\boxed{ \rm{ \:Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i} \: }} \\ \\ [/tex]

4. Mean using Step Deviation Method

[tex]\boxed{ \rm{ \:Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h \: }} \\ \\ [/tex]