Exercise 14.1 9 Questions – Mean by Direct Method
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).
xáµ¢: 110,130,150,170,190. Σfáµ¢xáµ¢ = 1320+1820+1200+1020+1900 = 7260. Σfáµ¢ = 50. xÌ„ = 7260/50 = ₹145.20
Q3: Mean age of 100 students. Use direct method with class marks. â†' Calculate Σfáµ¢xáµ¢/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. â†' Class mark = (45+55)/2=50 for first class etc. Σfáµ¢xáµ¢/35 ≈ 69.43%
Exercise 14.2 6 Questions – Assumed Mean & Step Deviation Method
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 uáµ¢=(xáµ¢âˆ'17)/h. Σfáµ¢uáµ¢ = ... Final mean ≈ 12.48 days
Q2: Find mean concentration of SOâ‚‚ in air (30 localities). â†' Use all three methods, verify answer matches.
Q5: Find mean number of days a student has attended school out of 220. â†' Use assumed mean or direct method.
Exercise 14.3 7 Questions – Mode & Median
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 (fâ‚=23). fâ‚€=21, fâ‚‚=14, l=15, h=5.
Mode = 15 + ((23âˆ'21)/(46âˆ'21âˆ'14))×5 = 15 + (2/11)×5 = 15 + 0.91 = 15.91 years
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.
Q3: Find mean, median, mode of shopping hours data. Compare them. â†' 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)
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
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. â†' x-coordinate at y=30 on less than curve.
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