Question

the median of the distribution given below is 137 find X and Y total frequency 68 in table class interval 65 -85 ,85-105 105-125, 125 - 1 45, 145 - 165 ,165 - 185 ,185 -250 so what and the frequency is 45 ,X ,20, 14,y 4​

Answer 1

Answer-the required equation is-$median = 85 + (68/X) * (45 - 45) / 20 = 85 + (68/X)$

Step-by-step explanation:

To find the median of a distribution, we need to order the data and find the middle value. In this case, we know that the total frequency is 68, so we can find the median by determining which class interval contains the 34th observation (since 68 is an even number, the median will be the average of the 34th and 35th observations).

Here's how you can find the median:

Start by ordering the class intervals from lowest to highest. In this case, the class intervals are: 65 - 85, 85 - 105, 105 - 125, 125 - 145, 145 - 165, 165 - 185, 185 - 250.

Determine the cumulative frequency of each class interval by adding up the frequencies of all the preceding intervals. The cumulative frequency of the first class interval is the same as its frequency. For example:

$65 - 85$$=45$

$85 - 105=45 + X$

$105 - 125=45 + X + 20$

$125 - 145=45 + X + 20 + 14$

$145 - 165=45 + X + 20 + 14 + Y$

$165 - 185=45 + X + 20 + 14 + Y + 4$

$185 - 250= 68$

Look for the class interval that contains the 34th observation. This will be the interval where the cumulative frequency is less than 34 and the next cumulative frequency is greater than or equal to 34. In this case, it is the $(45+X)$th interval.

To find the median, use the formula for the median of a grouped data:

$median = L + (n/f) * (Cf - F) / i$

where:

L = lower class limit of the median class

n = total frequency

f = frequency of the median class

Cf = cumulative frequency of the class preceding the median class

F = frequency of the class preceding the median class

i = width of the median class interval

For this problem,

L = lower class limit of 85-105

n = 68

f = frequency of the class 85-105

Cf = 45

F = frequency of class 65-85

i = width of class interval = 20

so $median = 85 + (68/X) * (45 - 45) / 20 = 85 + (68/X)$

in the same way you can calculate the median of 35th observation

Now you have enough information to solve for X and Y.

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Answer 2

Answer-the required equation is-

Step-by-step explanation:

To find the median of a distribution, we need to order the data and find the middle value. In this case, we know that the total frequency is 68, so we can find the median by determining which class interval contains the 34th observation (since 68 is an even number, the median will be the average of the 34th and 35th observations).

Here's how you can find the median:

Start by ordering the class intervals from lowest to highest. In this case, the class intervals are: 65 - 85, 85 - 105, 105 - 125, 125 - 145, 145 - 165, 165 - 185, 185 - 250.

Determine the cumulative frequency of each class interval by adding up the frequencies of all the preceding intervals. The cumulative frequency of the first class interval is the same as its frequency. For example:

Look for the class interval that contains the 34th observation. This will be the interval where the cumulative frequency is less than 34 and the next cumulative frequency is greater than or equal to 34. In this case, it is the th interval.

To find the median, use the formula for the median of a grouped data:

where:

L = lower class limit of the median class

n = total frequency

f = frequency of the median class

Cf = cumulative frequency of the class preceding the median class

F = frequency of the class preceding the median class

i = width of the median class interval

For this problem,

L = lower class limit of 85-105

n = 68

f = frequency of the class 85-105

Cf = 45

F = frequency of class 65-85

i = width of class interval = 20

so

in the same way you can calculate the median of 35th observation

Now you have enough information to solve for X and Y.

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