contestada

Here is some information about 26 houses.a,b and c are all different numbers.Number of bedrooms:1,2,3,4,5.Number of houses:7,a,b,c,8.The median number of bedrooms is 3.5 Work out a possible set of values for a,b and c.

Respuesta :

MrRoyal

Answer:

[tex][a,b,c]=[4,2,5][/tex] or [tex][a,b,c]=[2,4,5][/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{cccccc}{Bedroom} & {1} & {2} & {3} & {4} & {5} \ \\ {Houses} & {7} & {a} & {b} & {c} & {8} \ \end{array}[/tex]

[tex]n = 26[/tex]

[tex]Median = 3.5[/tex]

Required

Find a, b and c

Median is calculated as:

[tex]Median = \frac{n+1}{2}[/tex]

[tex]Median = \frac{26+1}{2}[/tex]

[tex]Median = \frac{27}{2}[/tex]

[tex]Median = 13.5th[/tex]

This means that the median is the average of the 13th and 14th item.

[tex]\begin{array}{cccccc}{Bedroom} & {1} & {2} & {3} & {4} & {5} \ \\ {Houses} & {7} & {a} & {b} & {c} & {8} \ \end{array}[/tex]

Since the median is [tex]Median = 3.5[/tex] (average of 3 and 4),

and:

[tex]3 \to b \to 13[/tex]

[tex]4 \to c \to 14[/tex]

This implies that c begins at 14

So, the number of houses bedrooms 4 and 5 is:

[tex]c + 8 = 26 - 14 +1[/tex]

[tex]c + 8 = 13[/tex]

[tex]c = 5[/tex]

Also

[tex]7 + a + b + c + 8 = 26[/tex] ---- sum of total frequency

[tex]a + b + c = 26 - 7 - 8[/tex]

[tex]a + b + c = 11[/tex]

Substitute [tex]c = 5[/tex]

[tex]a + b + 5 = 11[/tex]

[tex]a + b = 11 - 5[/tex]

[tex]a + b = 6[/tex]

Since a, b and c are different, then

a and b cannot be 5 because [tex]c = 5[/tex]

a and b cannot be 3 because [tex]a = b =3[/tex]

[tex]b \ne 0[/tex] because b ends at 13

a

So, possible sets are:

[tex][a,b]=[2,4][/tex]

[tex][a,b]=[4,2][/tex]

Include c, we have:

[tex][a,b,c]=[4,2,5][/tex] or [tex][a,b,c]=[2,4,5][/tex]

mickymike92

The possible set of values for a, b and c are:

{a,b,c} = {2,4,5} or {a,b,c} = {4,2,5}

The information provided about the houses is as follows:

  • number of houses, n = 26
  • median number of bedrooms = 3.5
  • Number of bedrooms:  1, 2, 3, 4, 5
  • Number of houses      : 7, a, b, c, 8

So;

  • 7 houses have 1 bedroom
  • a houses have 2 bedrooms
  • b houses have 3 bedrooms
  • c houses have 4 bedrooms
  • 8 houses have 5 bedrooms

median = (n + 1) / 2

median = 26 + 1 / 2

median = 13.5

Therefore, the median number of bedrooms is the average of the 13th and 14th houses.

Also, median = 3.5 = 3 + 4/ 2

Therefore, b = 13th house; c = 14th house

Since, n = 26 and c is the beginning of the 14th house;

c + 8 = 13

c = 13 - 8

c = 5 houses

Also; 7 + a + b = 13 houses

a + b = 13 - 7

a + b = 6 houses

  • Since a, b and c are different numbers; neither a or b can be 1 or 5
  • Since the 13th house marks the end of b; neither b nor a can be 0 or 6

The two possible sets of values of a and b are;

a = 2 and b = 4 or a = b and b = 2

Therefore, the possible set of values for a, b and c are:

{a,b,c} = {2,4,5} or {a,b,c} = {4,2,5}

Learn more about value sets and median at: https://brainly.com/question/22023

ACCESS MORE
ACCESS MORE
ACCESS MORE
ACCESS MORE

Otras preguntas