For an asymmetric distribution, if the mean and median are 20 and 30, then the value of the mode is:
50
For a moderately asymmetric (skewed) distribution, the empirical relationship between mean, median, and mode is given by Karl Pearson's formula:
\(\text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean}\)
Given: Mean = 20 and Median = 30. Substituting these values:
\(\text{Mode} \approx 3 \times 30 - 2 \times 20\)
\(\text{Mode} \approx 90 - 40 = 50\)
Therefore, the value of the mode is 50.
Similar Questions
The average of 25 numbers is 36. If the average of first 13 numbers is 32 and that of the last 13 numbers is 39, then the 13th number is
Calculate the mode of the following frequency distribution
Seconds
51-55
56-60
61-65
66-70
Frequency
2
7
8
4
The approximate harmonic mean of 8, 6, 12, 4 is:
The mode (correct to two decimal places) for the given data is:
Class- interval
Frequency
0-10
6
10-20
9
20-30
8
30-40
14
40-50
28
50-60
20
60-70
11
70-80
9
The arithmetic mean of marks of the students for the given data is:
Marks
No. of students
0-10
12
10-20
18
20-30
27
30-40
20
40-50
17
50-60
60
The incomes of the employees in a state is assumed to be normally distributed with mean Rs.15,000 and variance Rs. 900. The median of the distribution of the income is:
If the median of the observations 2, 3, 5, 6, x, 8, 9, is 6 then x CANNOT be equal to:
For a moderately skewed distribution, let mode = 15, median = 17.4. The value of mean is:
For the data set with the following observations, the first and second quartiles are:
20, 22, 23, 22, 23, 22, 22, 21, 19, 22, 22, 26, 23, 24, 19, 21, 22, 16
For a data set with 24 observations given below, the median is:
10, 11, 13, 13, 18, 20, 22, 22, 24, 24, 25, 29, 30, 31, 35, 37, 37, 37, 46, 51, 54, 55, 61, 64
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?
