Question

Calculate the median of the following frequency distribution:

x	8	9	10	11	12	13	14	15
fi	1	2	1	5	6	5	7	3

Answer 1

Step 1: Create a cumulative frequency table.

The cumulative frequency (cf) is the running total of the frequencies.

x (Value)	fi (Frequency)	Cumulative Frequency (cf)
8	1	1
9	2	3
10	1	4
11	5	9
12	6	15
13	5	20
14	7	27
15	3	30

Step 2: Find the total number of observations (N).

Summing all the frequencies:

N = 1 + 2 + 1 + 5 + 6 + 5 + 7 + 3

N = 30

Step 3: Determine the median position.

Since N is even (N = 30), the median is the average of the two middle values the `(N/2)^(th)` term and the `(N/2 + 1)^(th)` term.

First middle position: `30/2` = 15^th term

Second middle position: 15 + 1 = 16^th term

Step 4: Locate the values and calculate the median.

By looking at the cumulative frequency (cf) column:

The 15th term corresponds to x = 12 because the cumulative frequency reaches exactly 15 at this value.

The 16th term corresponds to x = 13 because values from the 16th to the 20th position are all 13.

Now, we find the average of these two values:

Median = `(12 + 13)/2`

 = 12.5

The median of the frequency distribution is 12.5.