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?
55
The empirical relation is Mode = 3 Median – 2 Mean, so \(\text{Median} = \frac{\text{Mode} + 2\,\text{Mean}}{3}\).
For the original data: \(\text{Median} = \frac{20 + 2 \times 15}{3} = \frac{50}{3}\).
When every value is multiplied by 3 and then increased by 5, the mean, median and mode all undergo the same change: new value = 3 × old value + 5.
New median = \(3 \times \frac{50}{3} + 5 = 50 + 5 = 55\).
Check: new mean = 3 × 15 + 5 = 50 and new mode = 3 × 20 + 5 = 65; then 3 × 55 – 2 × 50 = 165 – 100 = 65, so the empirical relation holds for the new data too.
Hence, 55.
Similar Questions
In an exam, marks scored by 16 students of section A (out of 50) are 33, 41, 56, 51, 53, 46, 49, 41, 45, 56, 51, 49, 46, 41, 53, 33 and marks scored by 13 students of section B (out of 50) are 47, 54, 42, 50, 47, 39, 42, 52, 56, 49, 54, 39, 47. Calculate the difference between the mode of section B and section A.
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?
Find the weighted mean of 15, 20 and 25 with weights 2, 3 and 5, respectively.
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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.
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.
The median of a symmetric distribution is 32 and the mode is 29. What is the mean?
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:
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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?
