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Solution - Statistics

Sum: 188
188
Arithmetic mean: x̄=26.857
x̄=26.857
Median: 24
24
Range: 59
59
Variance: s2=384.143
s^2=384.143
Standard deviation: s=19.600
s=19.600

Other Ways to Solve

Statistics

Step-by-step explanation

1. Find the sum

Add all the numbers:

24+3+29+24+8+38+62=188

The sum equals 188

2. Find the mean

Divide the sum by the number of terms:

Sum
188
Number of terms
7

x̄=1887=26.857

The mean equals 26.857

3. Find the median

Arrange the numbers in ascending order:
3,8,24,24,29,38,62

Count the number of terms:
There are (7) terms

Because there is an odd number of terms, the middle term is the median:
3,8,24,24,29,38,62

The median equals 24

4. Find the range

To find the range, subtract the lowest value from the highest value.

The highest value equals 62
The lowest value equals 3

623=59

The range equals 59

5. Find the variance

To find the sample variance, find the difference between each term and the mean, square the results, add together all of the squared results, and divide the sum by the number of terms minus 1.

The mean equals 26.857

To get the squared differences, subtract the mean from each term and square the result:

(2426.857)2=8.163

(326.857)2=569.163

(2926.857)2=4.592

(2426.857)2=8.163

(826.857)2=355.592

(3826.857)2=124.163

(6226.857)2=1235.020

To get the sample variance, add together the squared differences and divide their sum by the number of terms minus 1

Sum:
8.163+569.163+4.592+8.163+355.592+124.163+1235.020=2304.856
Number of terms:
7
Number of terms minus 1:
6

Variance:
2304.8566=384.143

The sample variance (s2) equals 384.143

6. Find the standard deviation

The standard deviation of the sample equals the square root of the sample variance. This is why the variance is usually represented by a squared variable.

Variance: s2=384.143

Find the square root:
s=(384.143)=19.600

The standard deviation (s) equals 19.6

Why learn this

The science of statistics deals with the collection, analysis, interpretation, and presentation of data, particularly in the contexts of uncertainty and variation. Understanding even the most basic of concepts in statistics can help us better process and understand information that we encounter in our everyday lives! Additionally, more data is collected now, in the 21st century, than ever before in all of human history. As computers have become more powerful, they have made it easier to analyze and interpret ever-larger datasets. Because of this, statistical analysis is becoming increasingly important in many fields, allowing governments and companies to fully understand and react to data.

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