Directions:
Read the following case studies carefully and answer the questions that follow.
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Case Study 1: Health Checkup Camp
A medical camp was held in a school to impart health education and the importance of exercise to children. During this camp, a medical check of 35 students was done and their weights were recorded as follows:
Weight (in kg) Less than 38 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52 No. of Students 0 3 5 9 14 28 32 35 -
Find the median weight of the students.
Solution: (A) 46.5 kg
Step 1: Convert to frequency distribution. Classes: 38-40 (3), 40-42 (2), 42-44 (4), 44-46 (5), 46-48 (14), 48-50 (4), 50-52 (3).
Step 2: $N=35, N/2=17.5$. CF just greater than 17.5 is 28. Median class is 46-48.
Step 3: $l=46, h=2, f=14, cf=14$. Median $= 46 + \frac{17.5 - 14}{14} \times 2 = 46 + \frac{3.5}{7} = 46 + 0.5 = 46.5$ kg. -
Find the modal weight of the students.
Solution: (C) 46.95 kg
Step 1: Max frequency is 14. Modal class is 46-48.
Step 2: $l=46, f_1=14, f_0=5, f_2=4, h=2$.
Step 3: Mode $= 46 + \frac{14-5}{2(14)-5-4} \times 2 = 46 + \frac{9}{19} \times 2 = 46 + \frac{18}{19} \approx 46.95$ kg.
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Find the median weight of the students.
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Case Study 2: Mileage of Cars
The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:
Mileage (km/l) 10-12 12-14 14-16 16-18 No. of Cars 7 12 18 13 -
Find the mean mileage of the cars.
Solution: (A) 14.48 km/l
Step 1: $x_i$: 11, 13, 15, 17. $f_i$: 7, 12, 18, 13.
Step 2: $f_i x_i$: 77, 156, 270, 221. $\sum f_i x_i = 724$. $\sum f_i = 50$.
Step 3: Mean $= 724/50 = 14.48$ km/l. -
Find the median mileage.
Solution: (B) 14.67 km/l
Step 1: $N=50, N/2=25$. CF: 7, 19, 37, 50. Median class 14-16.
Step 2: $l=14, cf=19, f=18, h=2$.
Step 3: Median $= 14 + \frac{25-19}{18} \times 2 = 14 + \frac{6}{9} = 14 + 0.67 = 14.67$ km/l.
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Find the mean mileage of the cars.