For What Value of X, Is the Median of the Following Frequency Distribution 34·5?

Find the number where half the data is above and half is below, which in this case is 34.5, in the frequency distribution.

For what value of x, is the median of the following frequency distribution 34·5 ?

Answer:

To find the median of a frequency distribution, you first need to determine the cumulative frequency and then locate the median class.

Here's how you can do it:

1. Calculate the cumulative frequency for each class.
2. Find the class where the cumulative frequency just exceeds N/2, where N is the total frequency (which is the sum of all frequencies).
3. Use the formula for finding the median within a class.

Given the frequency distribution:

The total frequency (N) is 3 + 5 + 11 + 10 + x + 3 + 2 = 34 + x.

Calculate cumulative frequency:

Median class: The median class is the one in which the cumulative frequency just exceeds N/2, which is (34 + x) / 2 = 17 + x/2.

Since the cumulative frequency in the 20-30 class (19) is just below 17 + x/2 and the cumulative frequency in the 30-40 class (29) is just above 17 + x/2, the median class is 30-40.

Using the formula for finding the median within a class:

Median = L + [(N/2 - F) / f] * w,

where:

• L is the lower boundary of the median class (30 in this case)
• N is the total frequency
• F is the cumulative frequency of the class before the median class
• f is the frequency of the median class
• w is the width of the class interval

Plugging in the values:

34.5 = 30 + [(17 + x/2 - 19) / 10] * 10,

Solving for x:

4.5 = (17 + x/2 - 19),

4.5 = -2 + x/2,

6.5 = x/2,

x = 13.

So, the value of x for which the median of the frequency distribution is 34.5 is 13.