Answer :

Sure, let's find the mean, median, mode, and range step-by-step for the list of numbers: [tex]\(82, 23, 59, 94, 70, 26, 32, 83, 87, 94, 32\)[/tex].

### Mean:
The mean is the average of all the numbers. To find it, add all the numbers together and divide by the number of numbers.

1. Sum the numbers:
[tex]\[ 82 + 23 + 59 + 94 + 70 + 26 + 32 + 83 + 87 + 94 + 32 = 682 \][/tex]

2. Count the number of numbers:
[tex]\[ \text{There are 11 numbers} \][/tex]

3. Divide the sum by the number of numbers:
[tex]\[ \text{Mean} = \frac{682}{11} = 62.0 \][/tex]

### Median:
The median is the middle value when the numbers are listed in order. If there is an even number of observations, the median is the average of the two middle numbers.

1. Arrange the numbers in ascending order:
[tex]\[ 23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94 \][/tex]

2. Find the middle number:
Since there are 11 numbers (odd number), the median is the 6th number in this sorted list.
[tex]\[ \text{Median} = 70 \][/tex]

### Mode:
The mode is the number that appears most frequently in the list.

1. Look for the number that appears most often:
[tex]\[ 94 \text{ appears twice, which is more frequent than any other number} \][/tex]

So, the mode is:
[tex]\[ \text{Mode} = 94 \][/tex]

### Range:
The range is the difference between the highest and lowest numbers.

1. Identify the highest and lowest numbers:
[tex]\[ \text{Highest number} = 94 \][/tex]
[tex]\[ \text{Lowest number} = 23 \][/tex]

2. Subtract the lowest number from the highest:
[tex]\[ \text{Range} = 94 - 23 = 71 \][/tex]

### Summary:
- Mean: 62.0
- Median: 70
- Mode: 94
- Range: 71

These results indicate the central tendencies and spread of the given set of numbers.

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