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

a.

i) & ii) -> See Explanation Below

a.

iii) and

b.

i)

ii)

Step-by-step 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

Collect like terms

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

is gotten by multiplying number of pets by corresponding number of students

is the total number of students

So;

becomes

Substitute 6.4 for Mean

Multiply both sides by 40

Subtract 196 from both sides

Divide both sides by 2

Reorder

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

Using

and

Subtract both equations

Divide both sides by -2

Substitute 6 for y in

becomes

Subtract 6 from both sides

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 = 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

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,

step-by-step explanation: