Question 1

What is mean in statistics?

Accepted Answer

Mean is the average of all numbers. Formula: sum of all numbers ÷ count of numbers. Example: 2,4,6,8 → mean = (2+4+6+8)/4 = 20/4 = 5. The mean is the most commonly used measure of central tendency, but it can be affected by outliers (extremely high or low values). For example, in the dataset 1,2,3,4,100, the mean is 22, which doesn't represent the typical value well.

Question 2

What is median in statistics?

Accepted Answer

Median is the middle value when numbers are sorted. For odd count: middle number. For even count: average of two middle numbers. Example: 2,4,6,8,10 → median = 6. For even: 2,4,6,8 → median = (4+6)/2 = 5. Median is more robust than mean because it's not affected by outliers. In salary data with one very high earner, median gives a better picture of typical earnings.

Question 3

What is mode in statistics?

Accepted Answer

Mode is the most frequent number. Example: 2,3,4,4,5,6 → mode = 4. A dataset can have no mode (all numbers appear once) or multiple modes (bimodal, trimodal). Bimodal example: 1,1,2,2,3 → modes = 1 and 2 (bimodal). Mode is useful for categorical data where you want to know the most common category, like most popular color or most common diagnosis.

Question 4

What is the difference between mean, median, and mode?

Accepted Answer

Mean is average (sum ÷ count), median is middle value (50th percentile), mode is most frequent value. For skewed data, median is often better than mean. Example: Salaries: 30k,35k,40k,45k,500k → mean = 130k (skewed by outlier), median = 40k (better representation). In perfectly symmetrical distributions, mean = median = mode. Use mean for normally distributed data, median for skewed data, and mode for categorical data.

Question 5

What is range in statistics?

Accepted Answer

Range = highest value - lowest value. Example: 2,5,8,12,15 → range = 15-2 = 13. Range shows how spread out the data is, but it's sensitive to outliers. A single extreme value can make the range very large. More robust measures of spread include interquartile range (IQR) and standard deviation. Range is useful for quick, rough estimates of data spread.

Question 6

What is variance and standard deviation?

Accepted Answer

Variance measures how far each number is from the mean. Formula: Variance = Σ(x - mean)² / n. Standard deviation is the square root of variance (σ = √Variance). Example: Data 2,4,6,8, mean=5: Differences: -3,-1,1,3; Squared: 9,1,1,9; Variance = 20/4 = 5; Standard deviation = √5 ≈ 2.24. Lower standard deviation means data points are closer to the mean (more consistent). Higher standard deviation means more spread out.

Question 7

What is the interquartile range (IQR)?

Accepted Answer

IQR is the range between the 25th and 75th percentiles (middle 50% of data). Formula: IQR = Q3 - Q1 (Q3 = 75th percentile, Q1 = 25th percentile). Example: 2,4,6,8,10,12,14 → Q1 = 4, Q3 = 12, IQR = 8. IQR is more robust than range because it ignores outliers. It's used to identify outliers: any value below Q1 - 1.5×IQR or above Q3 + 1.5×IQR is considered an outlier.

Question 8

What is a normal distribution?

Accepted Answer

A normal distribution (bell curve) is symmetrical, with mean = median = mode in the center. Properties: 68% of data falls within ±1 standard deviation, 95% within ±2 standard deviations, 99.7% within ±3 standard deviations. Examples of normally distributed data: Heights, IQ scores, exam scores. Normal distribution is fundamental in statistics because many statistical tests assume normality. Data can be transformed if not normally distributed.

Question 9

How to identify outliers in data?

Accepted Answer

Outliers are extreme values that differ significantly from other observations. Detection methods: 1) IQR method: Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are outliers, 2) Z-score method: Values with |z| > 3 are outliers, 3) Visual inspection using box plots, 4) Scatter plots for bivariate data. Outliers should be investigated - they may be errors, legitimate extreme values, or indicate important phenomena. Don't automatically remove outliers without justification.

Question 10

What is the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and describe data (mean, median, mode, standard deviation, range). They tell you what the data shows. Inferential statistics use samples to make predictions about populations (hypothesis testing, confidence intervals, regression). Example: Descriptive - 'The average height of students is 170cm.' Inferential - 'Based on a sample, we predict that the average height of all students is between 168-172cm with 95% confidence.' Our calculator focuses on descriptive statistics.

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