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The number of pets 40 students own is recorded

Number of pets: 2 , 4, 6, 8, 10
Number of students: x, 2, y, 6, 14

a) (i) show that x+y=18
(ii) If the mean of the distribution is 6.4, show that x +3y =30
(iii) Hence, find the value of x and of y
b) Using your answers in (a) (iii), find
(i) the median,
(ii) the mode,
Of the distribution

User Divakar R
by
8.1k points

1 Answer

2 votes

Answer:

a.

i) & ii) -> See Explanation Below

a.

iii)
y = 6 and
x = 12

b.

i)
Median = 7

ii)
Mode = 10

Explanation:

Given

Number of pets: 2 , 4, 6, 8, 10

Number of students: x, 2, y, 6, 14

Total students = 40

Required

a) (i) show that x+y=18

Given that total number of students is 40;

This implies that


x + 2 + y + 6 + 14 = 40

Collect like terms


x + y = 40 - 14 - 6 - 2


x + y = 18

a) (ii) If the mean of the distribution is 6.4, show that x +3y =30

The mean of a distribution is calculated as thus


Mean = (\sum fx)/(\sum x)


\sum fx} is gotten by multiplying number of pets by corresponding number of students


\sum fx} = 2 * x + 4 * 2 + 6 * y + 8 * 6 + 10 * 14


\sum fx} = 2 x + 8 + 6y + 48 + 140


\sum fx} = 2 x + 6y + 48 + 140+ 8


\sum fx} = 2 x + 6y + 196


\sum x} is the total number of students


\sum x} = 40

So;


Mean = (\sum fx)/(\sum x) becomes


Mean = (2 x + 6y + 196)/(40)

Substitute 6.4 for Mean


6.4 = (2 x + 6y + 196)/(40)

Multiply both sides by 40


256 = 2 x + 6y + 196

Subtract 196 from both sides


256 -196= 2 x + 6y + 196-196


60= 2 x + 6y

Divide both sides by 2


(60)/(2)= (2 x)/(2) + (6y)/(2)


30 = (2 x)/(2) + (6y)/(2)


30 = x + 3y

Reorder


x + 3y = 30

a) (iii) Hence, find the value of x and of y

Using


x + y = 18 and


x + 3y = 30

Subtract both equations


(x + y = 18) - (x + 3y = 30)


x - x + y - 3y = 18 - 30


y - 3y = 18 - 30


-2y = -12

Divide both sides by -2


(-2y)/(-2) = (-12)/(-2)


y = (-12)/(-2)


y = 6

Substitute 6 for y in
x + y = 18


x + y = 18 becomes


x + 6 = 18

Subtract 6 from both sides


x + 6 - 6 = 18 - 6


x = 12

b.

i) Calculate the Median

First, we need to tabulate the given data properly

Number of Pets ------ Number of students ------- Cumulative Frequency

2 ------------------------------12 -----------------------------------12

4 ------------------------------2 -----------------------------------14

6 ------------------------------6 -----------------------------------20

8 ------------------------------6 -----------------------------------26

10 ------------------------------14 -----------------------------------40

Since the number of pets is already arranged in ascending order,

the next step is to calculate the median element

Number of students = 40


Median = (40)/(2)

Median = 20

Given that number of students (40) is an even number,

The median is the average of the 20th and 21st element

From the table above; the median can be gotten from

6 ------------------------------6 -----------------------------------20

8 ------------------------------6 -----------------------------------26

The 20th element = 6

The 21st element = 8


Median = (6 + 8)/(2)


Median = (14)/(2)


Median = 7

ii) Mode

The mode is the corresponding data with the highest frequency

The highest frequency is 14;

The number of pets with frequency of 14 is 10

Hence,


Mode = 10

User Jeffgabhart
by
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