Statistical Calculations

Question 1

How do you calculate range

Answer 1

Range = Max (𝑥𝑖) − Min (𝑥𝑖)

1. Identify the maximum value in your data
2. Identify the minimum value in your data
3. Subtract the minimum from the maximum.

Question 2

How do calculate sample variance

Answer 2

𝑠² = (∑(𝑥𝑖 − x̄)²) / 𝑛 −1

1. Calculate the mean x̄ of the data
2. Subtract the mean from each data point to get the deviation
3. Square each deviation
4. Sum all the squared deviations
5. Divide the sum by (sample size minus 1) to get the sample variance.

Question 3

How do you calculate the standard deviation

Answer 3

𝑠 = √ 𝑠²
1. Find the sample variance 𝑠²
2. Take the square root of the sample variance to find the sample standard deviation

Question 4

How do you calculate the IQR

Answer 4

IQR = Q₁ − Q₃

1. Sort your data in ascending order
2. Find Q₁ (the 25th percentile) - the value below which 25% of the data lies
3. Find Q₃ (the 75th percentile) - the value below which 75% of the data lies
4. Subtract Q₁ from Q₃ to get the Interquartile Range (IQR)

Question 5

How do you calculate population variance

Answer 5

Formula (Population Variance):
𝜎² = ∑(𝑥𝑖 − 𝜇)² / 𝑁

Where:
𝜇 is the population mean (average of the entire population).
𝑁 is the population size (total number of data points in the population).

1. Find the population mean 𝜇
2. Subtract the population mean from each data point: (𝑥𝑖 − 𝜇)
3. Square each deviation
4. Sum all squared deviations
5. Divide the sum by 𝑁 (the total population size) to get the population variance 𝜎²

Question 6

How do you calculate standard error

Answer 6

SE = 𝑠 / √ 𝑛
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1. Find the sample standard deviation 𝑠
2. Find the sample size 𝑛
3. Divide 𝑠 by the square root of 𝑛 to get the standard error.

Question 7

How do you calculate coefficient of variation

Answer 7

CV = (𝑠 / x̄) x 100%

1. Find the sample standard deviation 𝑠
2. Find the sample mean x̄
3. Divide 𝑠 by x̄ then multiply by 100 to get the coefficient of variation as a percentage.

Question 8

How do you calculate a 95% confidence interval

Answer 8

CI = x̄ ± z x (𝑠 / √ 𝑛)
Where:
x̄ = Sample mean
𝑧 = Z-value corresponding to a 95% confidence level (approximately 1.96 for a normal distribution)
𝑠 = sample standard deviation
𝑛 = sample size

1. Calculate the sample mean
2. Calculate the sample standard deviation
3. Find the Z-value for 95% confidence (typically 1.96)
4. Calculate the Standard Error
5. Multiply the Z-value by the Standard Error to get the margin of error
6. Calculate the Confidence Interval by adding and subtracting the margin of error from the sample mean