Business Statistics: Central Tendency, Dispersion, Correlation and Regression (Basics) Questions

Question 1

Define statistics.

Accepted Answer

Statistics is the science of collecting, classifying, presenting, analyzing and interpreting numerical data.

Question 2

What is mean?

Accepted Answer

Mean is arithmetic average: Σx/n.

Question 3

Define standard deviation.

Accepted Answer

Standard deviation is the square root of variance and measures spread around mean.

Question 4

What is correlation?

Accepted Answer

Correlation measures degree and direction of relationship between two variables.

Question 5

What is regression?

Accepted Answer

Regression is a statistical method used to estimate/predict one variable from another.

Question 6

State formula of CV.

Accepted Answer

CV = (SD/Mean) × 100.

Question 7

Compute mean of 10, 12, 14, 14, 20.

Accepted Answer

Sum = 10+12+14+14+20 = 70. Mean = 70/5 = 14.

Question 8

Find median and mode of 10, 12, 14, 14, 20.

Accepted Answer

Ordered data: 10,12,14,14,20. Median = 14 (middle). Mode = 14 (highest frequency).

Question 9

Compute range of 5, 9, 12, 20.

Accepted Answer

Max = 20, Min = 5. Range = 20 − 5 = 15.

Question 10

Compute variance and SD for data 2, 4, 6.

Accepted Answer

Mean = 4. Deviations: −2,0,+2. Squares: 4,0,4. Sum = 8.
Variance = 8/3 = 2.667. SD = √2.667 ≈ 1.633.

Question 11

Explain why median is preferred over mean in presence of extreme values.

Accepted Answer

Mean uses all values and is affected by extreme observations (outliers). Median depends only on the middle position, so it is more stable in skewed data. Hence median is preferred when extreme values distort the mean.

Question 12

What is the meaning of r = 0 and r = −1 in correlation?

Accepted Answer

r = 0 indicates no linear correlation between variables. r = −1 indicates perfect negative correlation, meaning variables move exactly in opposite directions.

Question 13

Explain measures of central tendency (mean, median, mode) with merits and uses.

Accepted Answer

Measures of central tendency show a representative or central value of a dataset.

1) Arithmetic Mean:
Mean = Σx / n
Merits: simple, uses all values.
Demerits: affected by extreme values.

2) Median:
Median is the middle value after arranging data.
Merit: not much affected by extreme values; useful for skewed data.

3) Mode:
Mode is the most frequently occurring value.
Useful in business to find most popular size/brand or most demanded item.

Thus mean, median and mode help summarize data into one typical value for comparison and decisions.

Question 14

Explain standard deviation and show its calculation with an example.

Accepted Answer

Standard deviation (SD) is an important measure of dispersion that shows how much observations deviate from the mean.

Steps for ungrouped data:
1) Find mean (x̄).
2) Find deviations (x − x̄).
3) Square deviations and sum them: Σ(x − x̄)^2.
4) Variance = Σ(x − x̄)^2 / n.
5) SD = √variance.

Example: Data 2, 4, 6.
Mean = 4. Deviations: −2,0,+2. Squares: 4,0,4. Sum = 8.
Variance = 8/3 = 2.667.
SD = √2.667 ≈ 1.633.

Interpretation: Higher SD means higher variability and less stability/riskier series.

Question 15

Explain correlation and regression and mention their business applications.

Accepted Answer

Correlation measures the degree and direction of relationship between two variables.
- Positive correlation: variables move together.
- Negative correlation: one increases as the other decreases.
Pearson correlation coefficient r lies between −1 and +1.

Regression is used for prediction/estimation.
- Regression of Y on X predicts Y for given X.
- Regression of X on Y predicts X for given Y.

Business applications:
- Correlation: study relationship between advertising and sales.
- Regression: predict sales from advertising expenditure or demand from price.

Important note: correlation does not imply causation; it only indicates association.

Business Statistics: Central Tendency, Dispersion, Correlation and Regression (Basics)

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