Question

Given below is the distribution of 140 candidates obtaining marks X or higher in it certain examination in certain examination (all marks are given in whole numbers). Calculate the median of the distribution. x: 10 20 30 40 50 60 70 80 90 100 c.f. 140 133 118 100 75 45 15 9 2
Answer

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The median of this distribution of 140 candidates is 85.

To Find:

• The median of the distribution

Given:

• The distribution of 140 candidates who obtained marks in a certain examination.
• The marks obtained by the candidates (in whole numbers) and their cumulative frequency (c.f.) are given in the table: x: 10 20 30 40 50 60 70 80 90 100 c.f. 140 133 118 100 75 45 15 9 2

Solution:

The median of a distribution is the value that separates the higher half from the lower half of the data. To find the median of the distribution given, we need to use the cumulative frequency (c.f.) of each mark to determine the position of the median.

The cumulative frequency is the sum of the frequencies of all the marks up to a certain mark. In this case, the cumulative frequency of the mark 70 is 15, which means that 15 candidates scored 70 marks or lower. To find the median, we need to find the cumulative frequency that is greater than or equal to half of the total number of candidates (140/2 = 70).

Since the cumulative frequency of 70 is 15, which is less than 70, we need to look for the next higher mark. The cumulative frequency of the next higher mark, 80, is 9, which is still less than 70. But the cumulative frequency of 90, which is 2, is greater than 70.

Therefore, the median of this distribution would be between marks 80 and 90. To find the exact median, we can use the formula:

Median = L + (N/2 - C.F) / f * h

Where L is the lower class boundary, N is the total number of candidates, C.F is the cumulative frequency of the class preceding the median class, f is the frequency of the median class, and h is the class width.

In this case, the lower class boundary of the class containing the median is 80, the cumulative frequency of the preceding class (70) is 15, the frequency of the median class (80 - 90) is 9, and the class width is 10.

So, the median would be:

Median = 80 + (70 - 15) / 9 * 10 = 80 + 55/9 = 85

Therefore, the median of this distribution of 140 candidates is 85.

#SPJ2