Here are ten numbers
3 ,7,2,4,7,5,7,1,8,8
(a) write down the mode
(b) Work out the median
(c) Calculate the mean
(d) What is the range ?
The Correct answer and Explanation is:
Let’s analyze the given set of numbers: 3, 7, 2, 4, 7, 5, 7, 1, 8, 8. We will calculate the mode, median, mean, and range of these numbers.
(a) Mode
The mode is the number that appears most frequently in a data set. In our case, we have:
- 1: appears 1 time
- 2: appears 1 time
- 3: appears 1 time
- 4: appears 1 time
- 5: appears 1 time
- 7: appears 3 times
- 8: appears 2 times
The mode of this set is 7, as it occurs most frequently.
(b) Median
To find the median, we need to arrange the numbers in ascending order:
1, 2, 3, 4, 5, 7, 7, 7, 8, 8
Since there are 10 numbers (an even count), the median will be the average of the two middle numbers, which are the 5th and 6th numbers in this ordered list.
- The 5th number is 5.
- The 6th number is 7.
To find the median, we calculate the average of these two numbers:
[
\text{Median} = \frac{5 + 7}{2} = \frac{12}{2} = 6
]
(c) Mean
The mean is calculated by summing all the numbers and dividing by the count of the numbers:
[
\text{Sum} = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8 = 52
]
The count of the numbers is 10. Thus, the mean is:
[
\text{Mean} = \frac{52}{10} = 5.2
]
(d) Range
The range is determined by subtracting the smallest number from the largest number in the set.
- The smallest number is 1.
- The largest number is 8.
Thus, the range is calculated as follows:
[
\text{Range} = 8 – 1 = 7
]
Summary of Results
- Mode: 7
- Median: 6
- Mean: 5.2
- Range: 7
Explanation of Statistical Concepts
Understanding these basic statistics is crucial for interpreting data effectively. The mode gives insight into the most common value, useful in identifying trends or preferences within a dataset. The median provides a measure of central tendency that is not affected by extreme values (outliers), making it a reliable measure in skewed distributions. The mean, however, considers all values and can be influenced by outliers, providing a more comprehensive view of the average. Lastly, the range highlights the spread of the data, indicating the extent of variability. Each of these measures offers unique insights, and together they help to form a complete picture of the data set’s characteristics.