4, 6, 11, 17, 18, 3, 11, 21, 5, 11
Data Set Statistics Calculation
This guide explains how to compute the mean of the range and the mode using the provided data set.
Given Data
The data set provided is: 4, 6, 11, 17, 18, 3, 11, 21, 5, 11.
1. Range Calculation
To find the range, we first need the minimum and maximum values. Let's sort the data:
Sorted Data: 3, 4, 5, 6, 11, 11, 11, 17, 18, 21.
Minimum Value = 3
Maximum Value = 21
The range is calculated as:
\(Range = Maximum Value - Minimum Value\)
\(Range = 21 - 3 = 18\)
2. Mode Identification
The mode is the number that appears most often in the data set.
Observing the sorted data (3, 4, 5, 6, 11, 11, 11, 17, 18, 21), the number 11 occurs 3 times, more than any other number.
Mode = 11
3. Mean of Range and Mode Calculation
The final step is to calculate the mean of the range (18) and the mode (11).
Mean is calculated by summing the values and dividing by the count of values (which is 2 in this case).
\(Mean = (Value1 + Value2) / 2\)
\(Mean \ of \ Range \ and \ Mode = \frac{18 + 11}{2}\)
\(Mean \ of \ Range \ and \ Mode = \frac{29}{2}\)
\(Mean \ of \ Range \ and \ Mode = 14.5\)
Conclusion
The computed mean of the range and mode for the given data set is 14.5.
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
