15, 3, 8, 7, 6, 5, 5, 7, 18, 7
Understanding Data Measures: Mode, Median, and Mean
The question asks us to find the mean of the mode and the median for the dataset: 15, 3, 8, 7, 6, 5, 5, 7, 18, 7.
Calculating the Mode
The mode is the value that appears most frequently in the dataset. Let's count the occurrences of each number:
- 3: 1 time
- 5: 2 times
- 6: 1 time
- 7: 3 times
- 8: 1 time
- 15: 1 time
- 18: 1 time
The number 7 appears most often (3 times). Therefore, the mode is 7.
Determining the Median
To find the median, we first need to arrange the data in ascending order:
3, 5, 5, 6, 7, 7, 7, 8, 15, 18
There are 10 data points (an even number). The median is the average of the two middle values, which are the 5th and 6th values in the sorted list.
The 5th value is 7.
The 6th value is 7.
Median = \(\frac{7 + 7}{2} = \frac{14}{2} = 7\).
So, the median is 7.
Finding the Mean of Mode and Median
Now, we need to calculate the mean of the mode (7) and the median (7).
Mean = \(\frac{\text{Mode} + \text{Median}}{2}\)
Mean = \(\frac{7 + 7}{2} = \frac{14}{2} = 7\).
The mean of the mode and the median is 7.
Similar Questions
Find the median of the data 11, 16, 33, 15, 51, 19, 71, 75, 21, 17.
For a data, if the mean is 28.5 and the median is 32, then the mode using empirical formula is:
- If the mean of a distribution is 8.73 and its median is 11, then the mode of the distribution is __________ (using empirical relation).
- If the median and mode of a data of 20 numbers are 250 and 295, respectively, then find the sum of the 20 numbers.
- What is the mode of the following data?
70, 70, 73, 71, 74, 69, 80, 68, 66, 66, 89, 83, 81, 86, 82, 74, 86, 87, 67, 72, 62, 76, 86, 65, 62 - The median of \(\frac{3}{7}\), \(\frac{3}{5}\), \(\frac{11}{13}\), \(\frac{14}{16}\) and \(\frac{17}{19}\) is _____.
- What is the mode of the following data?
78, 60, 85, 76, 84, 86, 73, 89, 78, 77, 60, 63, 62, 72, 61, 78, 67, 77, 61, 78, 75, 61, 88, 66, 69 - What is the mode of the following data?
70, 79, 66, 89, 68, 80, 82, 80, 71, 84, 69, 68, 61, 85, 71, 84, 68, 86, 73, 75, 83, 88, 64, 88, 65 - The lifetime of certain species is given in the following table. Calculate the modal lifetime (rounded up to one decimal place) in days.
Lifetime (days) 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 10 35 52 61 38 29 - The given data shows the marks obtained by 50 students of a class in a test. What is the mean marks obtained by students?
Marks Number of Students 20 - 30 5 30 - 40 12 40 - 50 10 50 - 60 15 60 - 70 8
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.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
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
