Math Problem Statement

Cost of notebooks for these sample prizes: 7.95 9.98 5.58 4.99 10.75 6.25 7.63 8.50 8.88 please give the mean, median mode, range, mid range, standard deviation ,varian and coefficient of variation

Solution

Let's calculate the required statistics for the following sample notebook prices: 7.95, 9.98, 5.58, 4.99, 10.75, 6.25, 7.63, 8.50, 8.88.

1. Mean (Average)

The mean is calculated by summing all values and dividing by the number of data points: Mean=7.95+9.98+5.58+4.99+10.75+6.25+7.63+8.50+8.889\text{Mean} = \frac{7.95 + 9.98 + 5.58 + 4.99 + 10.75 + 6.25 + 7.63 + 8.50 + 8.88}{9}

2. Median

The median is the middle value when the data is arranged in order. First, we order the prices:
4.99,5.58,6.25,7.63,7.95,8.50,8.88,9.98,10.754.99, 5.58, 6.25, 7.63, 7.95, 8.50, 8.88, 9.98, 10.75 The middle value is the 5th one.

3. Mode

The mode is the value that appears most frequently. Since all prices appear only once, there is no mode.

4. Range

The range is the difference between the maximum and minimum values: Range=10.754.99\text{Range} = 10.75 - 4.99

5. Midrange

The midrange is the average of the maximum and minimum values: Midrange=10.75+4.992\text{Midrange} = \frac{10.75 + 4.99}{2}

6. Variance

Variance measures how far each number in the set is from the mean. It is calculated by: Variance=(x1xˉ)2+(x2xˉ)2++(xnxˉ)2n\text{Variance} = \frac{(x_1 - \bar{x})^2 + (x_2 - \bar{x})^2 + \cdots + (x_n - \bar{x})^2}{n} Where xˉ\bar{x} is the mean.

7. Standard Deviation

The standard deviation is the square root of the variance: Standard Deviation=Variance\text{Standard Deviation} = \sqrt{\text{Variance}}

8. Coefficient of Variation (CV)

The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage: CV=Standard DeviationMean×100\text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100

Now, let's calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any further questions or want to explore different concepts, feel free to ask!

Here are some questions you might be interested in:

  1. How do I calculate the mean of a set of numbers manually?
  2. Can you explain the concept of standard deviation in more detail?
  3. What is the significance of variance in data analysis?
  4. How is the coefficient of variation used in practical scenarios?
  5. What is the difference between mean, median, and mode?

Tip: The median is often a better measure of central tendency when dealing with skewed data or outliers.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion

Formulas

Mean = (Σx) / n
Median = middle value of the ordered data
Mode = most frequent value
Range = max - min
Midrange = (max + min) / 2
Variance = Σ(x - mean)^2 / n
Standard Deviation = √Variance
Coefficient of Variation = (Standard Deviation / Mean) * 100

Theorems

No specific theorems involved; general statistical calculations.

Suitable Grade Level

Grades 9-12