Given that the median of the numbers 15,8,11,21,32,5,25,7 is m. If 15 is replaced by 7, then the new median is n. Find the difference between m and n.
3.5
For an even count of numbers, the median is the mean of the two middle values after arranging the numbers in order.
Arranged: 5, 7, 8, 11, 15, 21, 25, 32. The 4th and 5th values are 11 and 15, so \(m = \frac{11 + 15}{2} = 13\).
Replacing 15 by 7 and arranging: 5, 7, 7, 8, 11, 21, 25, 32. The 4th and 5th values are 8 and 11, so \(n = \frac{8 + 11}{2} = 9.5\).
Difference = 13 – 9.5 = 3.5.
Check: in the new list three values (5, 7, 7) lie below 8 and three (21, 25, 32) lie above 11, so 8 and 11 are indeed the two middle values.
Hence, 3.5.
Similar Questions
A data set has a mean of 15 and a mode of 20. Each value is changed by multiplying by 3 and then adding 5. Assuming the empirical relation between the mean, median, and mode holds, what is the median of the new data set?
Find the weighted mean of 15, 20 and 25 with weights 2, 3 and 5, respectively.
The mean, median, and mode satisfy the empirical relation, Mode = 3×Median – 2×Mean. If the mean is increased by 5 while the median remains unchanged, then the new mode, will:
For a distribution, the empirical relation is, Mode = 3×Median – 2×Mean. If the Mean and Median satisfy, \(20 \le \text{Mean} \le 25\) and \(20 \le \text{Median} \le 25\), what is the possible range of the Mode?
The following figures give the temperature (in °C) of city X for a week in the month of March. Find the arithmetic mean (in °C) of the temperatures by the direct method.
Temperature recorded: 32.3, 34.5, 33.1, 32.7, 35.3, 33.2, 34.1
The median of the numbers, 5, 2x, 14, 18, 21 is 14. If x is positive integer, then number of possible values of x, is:
In a distribution, the mode is 18 and the mean is 22. Find the median. (Rounded off to 2 decimal places.)
The median of a symmetric distribution is 32 and the mode is 29. What is the mean?
The mode of a dataset is 25. Which of the following datasets has 25 as the unique mode?
The mean of a distribution is 72, and the mean exceeds the mode by 12. In this distribution, the value (Mean - Median) is one-third of (Mean - Mode). Find the median.
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?
The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the above data. The new median is:
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?
