Start Free Products PYQ Papers Blog About Enquiry API Profile Login
CBSE · NCERT

Class 10 Maths – Chapter 14: Statistics

Statistics helps organize, analyze, and interpret data. Learn three methods of finding the mean (Direct, Assumed Mean, Step Deviation), plus how to find the mode and median of grouped data, and draw ogives (cumulative frequency curves).

Exercises: 14.1–14.4·Total Questions: 25

Exercise 14.1 9 Questions – Mean by Direct Method

" Direct Method: x̄ = Σfᵢxᵢ / Σfᵢ. Find class mark xᵢ = (lower+upper)/2, multiply by frequency fᵢ, sum, divide by total frequency.
Q 1Daily Wages

A survey was conducted to find daily wages of workers. Find mean daily wages by direct method:

Wages: 100-120(12), 120-140(14), 140-160(8), 160-180(6), 180-200(10).

xᵢ: 110,130,150,170,190. Σfᵢxᵢ = 1320+1820+1200+1020+1900 = 7260. Σfᵢ = 50. x̄ = 7260/50 = ₹145.20

Q 2–9Applications

Q3: Mean age of 100 students. Use direct method with class marks. ' Calculate Σfᵢxᵢ/100 for given distribution.

Q5: Find mean number of mangoes per box. (Use step-deviation or direct.)

Q9: The following table gives literacy rate (in %) of 35 cities. Find mean literacy rate. ' Class mark = (45+55)/2=50 for first class etc. Σfᵢxᵢ/35 ≈ 69.43%

Exercise 14.2 6 Questions – Assumed Mean & Step Deviation Method

" Assumed Mean: x̄ = a + Σfᵢdᵢ/Σfᵢ where dᵢ=xᵢ'a. Step Deviation: x̄ = a + (Σfᵢuᵢ/Σfᵢ)—h where uᵢ=(xᵢ'a)/h.
Q 1Step Deviation

Find mean number of days a student was absent using step deviation method. Class: 0-6(11), 6-10(10), 10-14(7), 14-20(4), 20-28(4), 28-38(3), 38-40(1).

Let a=17, h (varies), but using step: Take a=17, calculate uᵢ=(xᵢ'17)/h. Σfᵢuᵢ = ... Final mean ≈ 12.48 days

Q 2–6All Three Methods

Q2: Find mean concentration of SO₂ in air (30 localities). ' Use all three methods, verify answer matches.

Q5: Find mean number of days a student has attended school out of 220. ' Use assumed mean or direct method.

Exercise 14.3 7 Questions – Mode & Median

" Mode: Mode = l + ((f₁'f₀)/(2f₁'f₀'f₂))—h. Median: Median = l + ((n/2'cf)/f)—h. l=lower limit of modal/median class, f₁=freq of modal class, f₀=freq before, f₂=freq after, cf=cumulative freq before median class.
Q 1Mode

Find mode of ages of 100 patients: 0-5(6), 5-10(11), 10-15(21), 15-20(23), 20-25(14), 25-30(5). Modal class = 15-20 (f₁=23). f₀=21, f₂=14, l=15, h=5.

Mode = 15 + ((23'21)/(46'21'14))—5 = 15 + (2/11)—5 = 15 + 0.91 = 15.91 years

Q 2Median

If median of distribution 60, find x and y: Given total frequency=50 and median class determined.

Build cf table. Median class is where cf ≥ n/2=25. Solve for x and y using total frequency constraint.

Q 3–7Applications

Q3: Find mean, median, mode of shopping hours data. Compare them. ' x̄≈75.8, median≈76.7, mode≈78.3. Mean < Median < Mode (negatively skewed).

Q5: Find median of student percentages.

Q7: Find mean, median, mode of distribution and compare.

Exercise 14.4 3 Questions – Ogives (Cumulative Frequency Curves)

" Ogive: Less than ogive – plot upper limit vs cumulative frequency. More than ogive – plot lower limit vs descending cumulative frequency. Intersection gives median.
Q 1Draw Ogive

The following distribution gives daily income of 50 workers. Convert to less than type and draw its ogive. Find median from graph.

Income: 100-120(12), 120-140(14), 140-160(8), 160-180(6), 180-200(10). Less than cf: 12, 26, 34, 40, 50. Plot points (120,12),(140,26)... Draw smooth curve. n/2=25, from graph median ≈ ₹138.50

Q 2–3Both Types

Q2: During medical check-up of 35 students, weights recorded. Draw less than and more than type ogives. Find median from graph.

Q3: Give less than ogive data, find median for 60 observations. ' x-coordinate at y=30 on less than curve.

Practice This Chapter

Generate unlimited practice questions for Statistics with Examzo AI-powered, faculty-validated, zero hallucinations.

Try PaperGenie → Take a Quick Test →

Statistics Practice?

Generate CBSE papers on mean, median, mode, and ogives.

Generate Practice Paper