Class 10 Mathematics: Statistics important questions

Statistics is a chapter of Class 10 Mathematics for the Andhra Pradesh State Board. These 10 questions are marked Very Important, Important or Practice, and each answer has been checked by our team. Use them to revise, not as a prediction of what will come in the exam.

1. Practice · 1 marks

   1. Assertion: The mode of sin 0°, cos 0°, sin 90° and tan 45° is 0. Reason: Mean x̄ = Σfᵢxᵢ / Σfᵢ. A) Both true, Reason supports Assertion B) Both true, Reason does not support Assertion C) Assertion true, Reason false D) Assertion false, Reason true

   D) The values are 0, 1, 1, 1, so the mode is 1, not 0: the Assertion is false. The Reason is the correct formula for the mean, so it is true.

2. Important · 2 marks

   2. Write the formula for the mean of grouped data by the direct method and explain the terms.

   Mean x̄ = Σfᵢxᵢ / Σfᵢ xᵢ = class mark (midpoint) of the ith class; fᵢ = frequency of the ith class; Σfᵢxᵢ = sum of the products of frequencies and class marks; Σfᵢ = total frequency.

3. Very Important · 8 marks

   3. The median of the following 60 observations is 28.5. Find x and y. Class: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60 Frequency: 5, x, 20, 15, y, 5

   Total: 5 + x + 20 + 15 + y + 5 = 60, so x + y = 15. The median 28.5 lies in the class 20–30: l = 20, h = 10, f = 20, cf = 5 + x, n/2 = 30. 28.5 = 20 + [(30 − 5 − x)/20] × 10 8.5 = (25 − x)/2 17 = 25 − x, so x = 8 and y = 15 − 8 = 7.

4. Important · 4 marks

   4. Write the formula to find the mode of grouped data and explain the terms in it.

   Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h l = lower limit of the modal class; f₁ = frequency of the modal class; f₀ = frequency of the class before it; f₂ = frequency of the class after it; h = class size.

5. Very Important · 8 marks

   5. A life insurance agent has this data on the ages of 100 policy holders. Policies are given only to persons aged 18 years and above but below 60. Find the median age. Age (years): below 20, below 25, below 30, below 35, below 40, below 45, below 50, below 55, below 60 Number of policy holders: 2, 6, 24, 45, 78, 89, 92, 98, 100

   Convert to classes: 18–20: 2, 20–25: 4, 25–30: 18, 30–35: 21, 35–40: 33, 40–45: 11, 45–50: 3, 50–55: 6, 55–60: 2. n = 100, n/2 = 50. The cumulative frequency first exceeds 50 in the class 35–40. l = 35, cf = 45, f = 33, h = 5. Median = 35 + [(50 − 45)/33] × 5 = 35 + 25/33 ≈ 35.76 years.

6. Very Important · 8 marks

   6. The daily expenditure on food of 25 households is: Expenditure (₹): 100–150, 150–200, 200–250, 250–300, 300–350 Households: 4, 5, 12, 2, 2 Choose a suitable method and find the mean daily expenditure on food.

   Using the direct method with class marks xᵢ = 125, 175, 225, 275, 325: fᵢxᵢ = 500, 875, 2700, 550, 650. Σfᵢ = 25, Σfᵢxᵢ = 5275. Mean = 5275/25 = ₹211. (The step-deviation method gives the same result and is quicker when the numbers are large.)

7. Important · 4 marks

   7. Write the formula for the median of grouped data. Explain the meaning of each symbol in the formula.

   Median = l + [(n/2 − cf)/f] × h l = lower limit of the median class n = total number of observations (sum of frequencies) cf = cumulative frequency of the class just before the median class f = frequency of the median class h = class size (width of the class)

8. Very Important · 8 marks

   8. The marks of 40 students in a Maths test are: Marks: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60 Students: 3, 5, 9, 10, 8, 5 i) Write the class mark xᵢ of each class. ii) Find fᵢxᵢ for each class. iii) Find the mean using the direct method.

   i) Class marks: 5, 15, 25, 35, 45, 55. ii) fᵢxᵢ: 3×5 = 15, 5×15 = 75, 9×25 = 225, 10×35 = 350, 8×45 = 360, 5×55 = 275. iii) Σfᵢ = 40, Σfᵢxᵢ = 15 + 75 + 225 + 350 + 360 + 275 = 1300. Mean = Σfᵢxᵢ / Σfᵢ = 1300/40 = 32.5 marks.

9. Important · 4 marks

   9. Write the formula for the mode of grouped data and give the meaning of each symbol.

   Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h l = lower limit of the modal class (the class with the highest frequency) f₁ = frequency of the modal class f₀ = frequency of the class before the modal class f₂ = frequency of the class after the modal class h = class size

10. Very Important · 8 marks

    10. Find the median weight of 30 students: Weight (kg): 40–45, 45–50, 50–55, 55–60, 60–65, 65–70, 70–75 Students: 2, 3, 8, 6, 6, 3, 2

    Cumulative frequencies: 2, 5, 13, 19, 25, 28, 30. n = 30, so n/2 = 15. The median class is 55–60 (the first class whose cumulative frequency exceeds 15). l = 55, cf = 13, f = 6, h = 5. Median = 55 + [(15 − 13)/6] × 5 = 55 + 10/6 = 56.67 kg (approx.).