Question

The mean of 3, 7, x, 9, 4, 2, y is 5 and their mode is 4. Find the values of x and y. Find also the median.

Answer 1

Answer:

Step-by-step explanation:

The data are as follows:

3, 7, x, 9, 4, 2, y.

Acc to the question mode is 4 that means either x = 4 or y = 4.

Let us assume x = 4 then,

3 + 7 + 4 + 9 + 4 + 2 + y = 29 + y

or, (29 + y)/7 = 5

or, 29 + y = 35

or, y = 6.

Therefore, either x = 4 & y = 6 or, x = 6 and y = 4.

Median will be:

2, 3 4, 4, 6, 7, 9.

Therefore, median will be 4. i.e. (n+1)/2th element.

Answer 2

Answer:

x = 4

y = 6

Median = 4

Step-by-step explanation:

Hi,

Given set of observations are 3, 7, x, 9, 4, 2, y

Number of Observations = 7

Given mean = 5

Mean is defined as sum of the observations/Number of observations

Mean = ( 25 + x + y)/7

5 = (25 + x + y)/7

25 + x + y = 35

x + y = 10

Given Mode = 4

Mode is defined as the observation with highest frequency.

SInce every known observation occurs once, hence atleast one of x or y

should be equal to 4

let x = 4

Thus using x + y = 10, we get y = 6

Thus the value of x and y are 4 and 6

Hence, the observations in increasing order are

2, 3, 4, 4, 6, 7 and 9

Clearly, we can observe that the middle observation is 4.

Median of an ungrouped data is defined as the middle observation.

Hence median of the given data is 4

Hope, it helps !