NumericalHard4 marks
The marks of 10 students of a class in an examination arranged in ascending order is as follows: 13, 35, 43, 46, x, x + 4, 55, 61, 71, 80 If the median marks is 48, find the value of x. Hence find the mode of the given data
Topic: Mean / median / mode / quartiles
Previous-year question practice database
Answer
Exam answer
Ordered data: 13, 35, 43, 46, x, x+4, 55, 61, 71, 80.
There are 10 observations.
Median = average of 5th and 6th observations.
48 = [x + (x+4)]/2 96 = 2x + 4 x = 46.
The data become: 13, 35, 43, 46, 46, 50, 55, 61, 71, 80.
Mode = 46.
Answer: x = 46; Mode = 46.
Explanation
For an even number of observations, median is the average of the two middle values. Then identify the value occurring most frequently.
More from Measure of Central Tendency (Mean, Median, Quartiles and Mode)
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