The mean and the mode of a set of data are 40.3 and 74.9, respectively. Find the median of the data, using the empirical formula. (Round off to one decimal place)
51.8
The empirical relationship between the three measures of central tendency for a moderately skewed distribution is: Mode = 3 × Median − 2 × Mean. Rearranging gives Median = (Mode + 2 × Mean) / 3.
Substituting the given values, Median = (74.9 + 2 × 40.3) / 3 = (74.9 + 80.6) / 3 = 155.5 / 3.
On dividing, Median = 51.833…, which rounds off to 51.8 (one decimal place).
Hence, the correct answer is 51.8.
Similar Questions
If the mode of a data exceeds its mean by 19.8, then the mode exceeds the median by ______. (Use empirical formula to find the answer.)
What is the mode of the following data?
41, 48, 54, 50, 54, 48, 42, 43, 48, 42, 53, 45, 44, 50, 49, 45, 43, 48, 42, 48
The mean and the mode of a set of data are 53.1 and 14.1, respectively. Find the median of the data, using the empirical formula.
If the mean of the following data is 42, then what is the value of x?
Class 10-20 20-30 30-40 40-50 50-60 Frequency 44 29 39 10 x From the following data, what is the value of the median?
18, 20, 21, 25, 26, 23 ,29 ,32, 41, 33, 39
If the mean of the following data is 47, then what is the value of x?
Class 20-30 30-40 40-50 50-60 60-70 Frequency 20 29 22 32 x Calculate mode from the given data.
Class Interval 0-5 5-10 10-15 15-20 20-25 Number of states 15 10 6 7 2 What is the value of \((2x + 4y)\), if mean of the following distribution is 42?
Class 0-20 20-40 40-60 60-80 80-100 Total Frequency 8 20 x 2 y 70 What is the value of (9x + 2y), if mean of the following distribution is 64?
Class 0-20 20-40 40-60 60-80 80-100 Total Frequency 8 20 x 6 y 80 The mean of a data set is 40 and the median is 35. Find the mode using the empirical relation.
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
The difference between the upper limit and the lower limit of a class is called :
