Consider the following discrete frequency distribution: x 1 2 3 4 5 6 7 8 f 3 15 45 57 50 36 25 9
4
Median Calculation for Discrete Frequency Distribution
Consider the following discrete frequency distribution:
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| f | 3 | 15 | 45 | 57 | 50 | 36 | 25 | 9 |
What is the value of median of the distribution?
To find the median of the discrete frequency distribution, we follow these steps:
Step 1: Calculate the total number of observations (N).
N = Sum of all frequencies (f)
N = 3 + 15 + 45 + 57 + 50 + 36 + 25 + 9
N = 240
Step 2: Calculate the cumulative frequency (Cf).
We need to construct a cumulative frequency table to easily locate the median.
| x | f | Cf (Cumulative Frequency) |
|---|---|---|
| 1 | 3 | 3 |
| 2 | 15 | 3 + 15 = 18 |
| 3 | 45 | 18 + 45 = 63 |
| 4 | 57 | 63 + 57 = 120 |
| 5 | 50 | 120 + 50 = 170 |
| 6 | 36 | 170 + 36 = 206 |
| 7 | 25 | 206 + 25 = 231 |
| 8 | 9 | 231 + 9 = 240 |
Step 3: Determine the median position and value.
For a discrete frequency distribution with an even total number of observations (N), the median is often defined as the value of 'x' corresponding to the first cumulative frequency that is greater than or equal to N/2.
Median Position = N / 2
Median Position = 240 / 2 = 120
Now, we find the smallest 'x' value in the cumulative frequency table for which Cf ≥ 120:
- For x = 1, Cf = 3 (3 < 120)
- For x = 2, Cf = 18 (18 < 120)
- For x = 3, Cf = 63 (63 < 120)
- For x = 4, Cf = 120 (120 ≥ 120)
The first value of x for which the cumulative frequency is greater than or equal to 120 is 4.
The final answer is 4.
Similar Questions
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
The numbers 4 and 9 have frequencies x and (x - 1) respectively. If their arithmetic mean is 6, then what is the value of x?
If M is the mean of n observations x 1- k, x 2- k, x 3- k, _ _ _, x n- k, where k is any real number, then what is the mean of x 1, x 2, x 3, _ _ _, x n?
The following tables gives the frequency distribution of number of peas per pea pod of 198 pods:
Number of peas
1
2
3
4
5
6
7
Frequency
4
33
76
50
26
8
1
What is the median of this distribution?What is the mean of the marks ?
What is the median of the marks?
What is the sum of the deviations measured from the median?
The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to ?
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9C9, respectively?
Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
If the difference of mode and median is 36, then the difference of median and mean is:
In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
The average of 25 numbers is 36. If the average of first 13 numbers is 32 and that of the last 13 numbers is 39, then the 13th number is
