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?

(a) Mode: The number that appears most frequently. 
- The number 7 appears three times, more than any other number.  
- Mode: 7

(b) Median: The middle value when the numbers are arranged in ascending order. 
- Arrange the numbers: 1, 2, 3, 4, 5, 7, 7, 7, 8, 8 
- For an even number of values, the median is the average of the two middle numbers. 
- The middle numbers are the 5th and 6th values: 5 and 7. 
- Median: \(\frac { 5 + 7} { 2} = 6\)

(c) Mean: The average of the numbers. 
- Sum of the numbers: \(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8 = 52\) 
- Number of values: 10 
- Mean: \(\frac { 52} { 10} = 5.2\)

(d) Range: The difference between the highest and lowest values. 
- Highest value: 8 
- Lowest value: 1 
- Range: \(8 - 1 = 7\)

Supplemental Knowledge:

Understanding the concepts of mode, median, mean and range are central to statistics. These measures serve as summarization tools by offering insights into data points' central tendency and variability.

1. Mode: 
The mode is the number that appears most frequently in a data set. A set can have more than one mode if multiple values appear with the same highest frequency (bimodal or multimodal).

2. Median: 
The median is the middle value when the numbers are arranged in ascending order. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, it’s the average of the two middle numbers.

3. Mean: 
The mean (or average) is calculated by adding all the numbers together and then dividing by the count of numbers.

4. Range: 
The range is the difference between the highest and lowest values in a data set.

Applied Knowledge:

Imagine you are analyzing customer satisfaction survey results for a new product: 
- If most customers rate your product as 7 (mode), it suggests general satisfaction. 
- If half rate it below 6 and half above 6 (median), you know where your central tendency lies. 
- An average rating (mean) might be 5.8, indicating overall moderate satisfaction. 
- A wide range from 1 to 10 suggests diverse opinions about your product.

Mastering statistical concepts like mode, median, mean, and range can significantly enhance your analytical skills. At UpStudy, we offer tools and resources that make learning these essential concepts straightforward and engaging, including a Statistics and probability calculator.

For those keen on deepening their understanding of statistics or seeking help with related topics, explore UpStudy’s live tutor question bank or our AI-powered problem-solving services today! Enhance your knowledge with us!