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Business Mathematics and Statistics · Class 11 Commerce

Ch 8Descriptive Statistics and Probability — Class 11 Business Mathematics and Statistics, concept-first.

Business decisions are constantly made from data — average sales, typical wages, the most common size of order — and the first job of statistics is to reduce a whole mass of raw numbers to a single representative figure.

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Key concepts

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Measures of Central Tendency

Measures of Central Tendency

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Measures of Central Tendency — Mean, Median and Mode

Business decisions are constantly made from data — average sales, typical wages, the most common size of order — and the first job of statistics is to reduce a whole mass of raw numbers to a single re…

2

Measures of Dispersion — Range, Standard Deviation and Coefficient of Variation

Two data sets can share the identical mean and still behave very differently — one tightly clustered around it, the other wildly spread out. Dispersion measures exactly this spread.

3

Basic Concepts of Probability — Random Experiments, Sample Space and Events

The second half of this chapter turns from describing past data to reasoning about uncertain future outcomes — the mathematics of chance itself, which underlies every business decision made under risk…

4

Addition Theorem of Probability

A frequent business question involves the probability that one event OR another occurs — will a customer buy product A or product B, will a machine fail due to fault X or fault Y.

5

Conditional Probability and Independent Events

Sometimes new information changes the probability of an event — knowing that a customer is a repeat buyer changes the probability they will buy again this month.

Exercises

+Show 5 questions5 questions
  1. Q6The wages (in ₹) of 7 workers in a small unit are: 8000, 9000, 9000, 10000, 11000, 9000, 12000. Find the mean, median and mode of the wages.Free
  2. Q7Find the standard deviation and coefficient of variation of the following data: 10, 12, 14, 16, 18.Free
  3. Q8A committee of 3 is to be selected at random from a group of 4 men and 3 women. Find the probability that the committee consists of exactly…Preview
  4. Q9In a class, 60% of the students are boys and 40% are girls. It is known that 5% of the boys and 10% of the girls are left-handed. A student…Preview
  5. Q10Two dice are rolled together. Find the probability of getting a total of 8 or a total of 10.Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 24 questions24 questions
  1. Q1If median = 45 and its co-efficient is 0.25, then the mean deviation about median is : (a) 45 (b) 11.25 (c) 180 (d) 0.0056Preview
  2. Q2Let a sample space of an experiment be $S = \{E_1, E_2, \ldots E_n\}$ then $\sum_{i=1}^{n} P(E_i)$ is equal to : (a) $\dfrac{1}{3}$ (b) $0$…Preview
  3. Q3If A and B are independent events $P(A) = \dfrac{2}{5}$ and $P(B) = \dfrac{1}{5}$ then $P(A \cap B)$ : (a) $0$ (b) $\dfrac{3}{25}$ (c) $\dfr…Preview
  4. Q4Calculate the Harmonic mean for the following values : $1, 45, 10, 4, 11.2$Preview
  5. Q5(a) A problem is given to 3 students X, Y and Z whose chances of solving it are $\dfrac{1}{2}$, $\dfrac{1}{3}$ and $\dfrac{2}{5}$ respective…Preview
  6. Q6If median $= 45$ and its co-efficient is $0.25$, then the mean deviation about median is : (a) $0.0056$ (b) $11.25$ (c) $45$ (d) $180$Preview
  7. Q7The probability of obtaining even prime number on each die, when a pair of dice is rolled is : (a) $\dfrac{1}{3}$ (b) $\dfrac{1}{36}$ (c) $\…Preview
  8. Q8If the outcome of one event does not influence another event then the two events are : (a) Not disjoint (b) Mutually exclusive (c) Independe…Preview
  9. Q9Let $P(A) = \dfrac{3}{5}$ and $P(B) = \dfrac{1}{5}$. Find $P(A \cap B)$ if A and B are independent events.Preview
  10. Q10Calculate the mean deviation about mean and its coefficient of the income groups of five, given below. | Income (₹) | 4,000 | 4,200 | 4,400…Preview
  11. Q11(a) Compute Quartile deviation from the following data. | C.I | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | | --- | --- | --- |…Preview
  12. Q12Which of the following represents Median ? (a) $Q_3$ (b) $Q_1$ (c) $D_2$ (d) $Q_2$Preview
  13. Q13The probability of drawing a spade from a pack of cards is : (a) $\dfrac{4}{13}$ (b) $\dfrac{1}{52}$ (c) $\dfrac{1}{4}$ (d) $\dfrac{1}{13}$Preview
  14. Q14An aeroplane flies, along the four sides of a square at speeds of 100, 200, 300 and 400 kilometres per hour respectively. Find the average s…Preview
  15. Q15Compute $Q_1$, $D_2$ and $P_{90}$ from the following data. | Marks | 10 | 20 | 30 | 40 | 50 | 60 | | --- | --- | --- | --- | --- | --- | ---…Preview
  16. Q16(a) A company has three machines A, B, C which produces 25%, 30% and 50% of the product respectively. Their respective defective percentages…Preview
  17. Q17Let $P(A)=\dfrac{3}{5}$ and $P(B)=\dfrac{1}{5}$. Find $P(A\cap B)$ if $A$ and $B$ are independent events. (a) $\dfrac{3}{16}$ (b) $\dfrac{3}…Preview
  18. Q18If two events $A$ and $B$ are dependent, then the conditional probability of $P(B/A)$ is : (a) $\dfrac{P(A\cap B)}{P(A)}$ (b) $P(A)\,P(B/A)$…Preview
  19. Q19Find $D_2$ and $D_6$ for the following series $22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8$.Preview
  20. Q20A person purchases tomatoes from each of the 4 places at the rate of 1 kg., 2 kg., 3 kg. and 4 kg. per rupee respectively. On the average, h…Preview
  21. Q21The correct relationship among A.M., G.M., and H.M., is : (a) $H.M \geq G.M \geq A.M$ (b) $A.M < G.M < H.M$ (c) $A.M \geq G.M \geq H.M$ (d)…Preview
  22. Q22If $Q_1=30$ and $Q_3=50$, the coefficient of Quartile deviation is : (a) $10$ (b) $20$ (c) $0.25$ (d) $40$Preview
  23. Q23An aeroplane flies along the four sides of a square at speeds of 100, 200, 300 and 400 kilometres per hour respectively. What is the average…Preview
  24. Q24(a) Three boxes $B_1$, $B_2$, $B_3$ contain Lamp bulbs some of which are defective. The defective proportions in box $B_1$, box $B_2$ and bo…Preview

More questions

+Show 5 questions5 questions
  1. Example 1Find the mean, median and mode of the following data on the number of complaints received per day at a customer-service desk over 9 days: 3,…Free
  2. Example 2Two salespersons, A and B, recorded the following daily sales (in ₹'000) over 5 days. A: 20, 22, 24, 26, 28 B: 15, 20, 25, 30, 35 Find the c…Free
  3. Example 3A card is drawn at random from a well-shuffled pack of 52 playing cards. Find the probability that the card drawn is (i) a king, (ii) a red…Preview
  4. Example 4A die is rolled once. Find the probability of getting an even number or a number greater than 4, using the addition theorem.Preview
  5. Example 5A bag contains 5 red balls and 3 black balls. Two balls are drawn one after another without replacement. Find the probability that both ball…Preview