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Nine conical flasks have sodium chloride solution of different quantities. The amount of solution \( (\mathrm{ml}) \) in each flask is given below. \( 2,10,16,2,20,18,22,14,9 \) Mean :_ Median :__ Mode :__ Range :

Ask by Edwards Vaughn. in the United States
Jan 27,2025

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Answer

- **Mean:** 12.56 ml - **Median:** 14 ml - **Mode:** 2 ml - **Range:** 20 ml

Solution

Let's analyze the given data to find the **Mean**, **Median**, **Mode**, and **Range**. ### Given Data: \[2, 10, 16, 2, 20, 18, 22, 14, 9\] ### Step 1: Organize the Data First, sort the data in ascending order: \[2, 2, 9, 10, 14, 16, 18, 20, 22\] ### Step 2: Calculate the Mean The **Mean** is the average of all the numbers. \[ \text{Mean} = \frac{\sum \text{values}}{\text{number of values}} = \frac{2 + 2 + 9 + 10 + 14 + 16 + 18 + 20 + 22}{9} = \frac{113}{9} \approx 12.56 \, \text{ml} \] ### Step 3: Determine the Median The **Median** is the middle value of the sorted data. Since there are 9 data points (an odd number), the median is the 5th value. \[ \text{Median} = 14 \, \text{ml} \] ### Step 4: Identify the Mode The **Mode** is the number that appears most frequently. In the sorted data, the number **2** appears twice, which is more than any other number. \[ \text{Mode} = 2 \, \text{ml} \] ### Step 5: Find the Range The **Range** is the difference between the maximum and minimum values. \[ \text{Range} = \text{Max} - \text{Min} = 22 - 2 = 20 \, \text{ml} \] ### Summary: - **Mean:** 12.56 ml - **Median:** 14 ml - **Mode:** 2 ml - **Range:** 20 ml

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The Deep Dive

To calculate the mean, median, mode, and range, let’s analyze the given data: \( 2, 10, 16, 2, 20, 18, 22, 14, 9 \). First, let's calculate the mean: Mean = \( \frac{\text{Sum of all values}}{\text{Total number of values}} \) Sum = \( 2 + 10 + 16 + 2 + 20 + 18 + 22 + 14 + 9 = 123 \) Mean = \( \frac{123}{9} = 13.67 \) (approximately) Next, let's find the median: To find the median, we first need to arrange the values in ascending order: \( 2, 2, 9, 10, 14, 16, 18, 20, 22 \) Since we have 9 values, the median is the middle value: Median = \( 14 \) Now, let's determine the mode: The mode is the number that appears most frequently. Here, \( 2 \) appears twice, while all other values appear only once. Mode = \( 2 \) Finally, let's calculate the range: Range = \( \text{Maximum Value} - \text{Minimum Value} \) Range = \( 22 - 2 = 20 \) **Summary of the calculations:** Mean: \( 13.67 \) Median: \( 14 \) Mode: \( 2 \) Range: \( 20 \)

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