Solve the following problem.The weights of the students in a class are the following: 69,70,75, 66, 83, 88, 66, 63, 61, 68, 73, 57, 52, 58, and 77. Calculate thefollowing:1. Qi2.033. Do4. Pas5. PROLearning Task 2Given the frequency distribution, compute for the third quartile, fourth decile, and 65th percentile.Class Intervalf<cf81-9076071-80105361-70154351-6042841-50122431-4061221-303611-20231-1011Himilation Time Frame: 30 minutes)
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Given :- problem.The weights of the students in a class are the following: 69,70,75, 66, 83, 88, 66, 63, 61, 68, 73, 57, 52, 58, and 77.
To Find :- Q1, Q3, D4 ?
Solution :-
Arranging data in ascending order = 52, 57, 58, 61, 63, 66, 66, 68, 69, 70, 73, 75, 77, 83, 88 = Total terms = 15 = n
now,
→ First Quartile (Q1) = {(n + 1)/4}th term .
→ Q1 = (15 + 1)/4 th term
→ Q1 = 16/4 = 4th term = 61 (Ans.)
and,
→ Third Quartile(Q3) = {3(n + 1)/4}th term .
→ Q3 = {3*(15 + 1)/4} th term
→ Q3 = (3 * 16/4) th term = 12th term = 75 (Ans.)
now,
→ Di = {(N + 1) * i} / 10 th term
→ D4 = {(15 + 1) * 4}/10 th term
→ D4 = (16 * 4)/10 th term
→ D4 = 6.4 th term
→ D4 = Between 6th and 7th term
→ D4 = 6th term + 0.4(7th term - 6th term)
→ D4 = 66 + 0.4(66 - 66)
→ D4 = 66 (Ans.)
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