find the median for the given frequency
score, x = 1,2,3,4,5,6,7,8,9,10
frequency, f = 1,1,3,3,5,7,5,5,7,1
1. n/2 = 38/2 =19
2) median is the mean of the 19th and 20th number.
Mean = 12/2 = 6
Help me with my questions
To find the median for the given frequency, you need to first create a cumulative frequency table. Here are the steps to follow:
Step 1: Arrange the scores (x) in ascending order.
x = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Step 2: Calculate the cumulative frequency (C.F.) by adding up the frequencies (f) from the beginning to each score.
Cumulative frequency table:
x | f | C.F.
---------------------
1 | 1 | 1
2 | 1 | 2
3 | 3 | 5
4 | 3 | 8
5 | 5 | 13
6 | 7 | 20
7 | 5 | 25
8 | 5 | 30
9 | 7 | 37
10 | 1 | 38
Step 3: Find the median position using the formula (N + 1) / 2, where N is the total frequency (sum of all frequencies).
N = 38
Median position = (38 + 1) / 2 = 39 / 2 = 19.5
Step 4: Locate the median position (19.5) in the cumulative frequency table. In this case, it falls between the cumulative frequencies of 8 and 13.
Step 5: Find the corresponding score for the median position by interpolating between the values.
Median score = L + ((N/2 - C) / f) * h
Where:
L = Lower boundary of the interval (cumulative frequency below the median position)
N = Total frequency
C = Cumulative frequency of the interval before the median position
f = Frequency of the interval containing the median position
h = Class width (in this case, the scores have a width of 1)
Using the values from the cumulative frequency table:
L = 4
N = 38
C = 8
f = 5
h = 1
Median score = 4 + ((19.5 - 8) / 5) * 1
= 4 + (11.5 / 5)
= 4 + 2.3
= 6.3
Therefore, the median for the given frequency is 6.3.