Page 217 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Unit-27: Measures of Central Tendency: Mean, Median, Mode

Marks obtained 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 note
number of 5 4 8 6 2 6 7 2
students

Solution: (A) Calculation of mode by inspection method-

Marks obtained number of students
0–10 5
10–20 4 (f )
1
20–30 8 (f)
30–40 6 (f )
2
40–50 2
50–60 6
60–70 7
70–80 2
in the given question the frequency of 8 is highest and its value is given in the class interval 20–30.
Therefore, to find the real value of this class interval we will use the given formula.
f − f
Mo = L + 1 × i i ×
2 f − f − 1 f 2
in this way
L = 20 (Lower limit of mode class-interval)
f = 8 (frequency of mode class-interval)
f = 4 (the frequency of class interval-before mode
1
class-interval)
f = 6 (the frequency of class-interval after mode
2
class-interval)

i = 10 (the difference between the upper and lower
limit of mode class-interval [30 – 20 = 10])
Putting the above values in the formula
−
84
Mo = 20 + × 10
−− 6
28 4
4
Mo = 20 + × 10
16 −− 6
4
41
Mo = 20 +
6
Mo = 20 + 6.67 = 26.67
therefore mode Mo = 26.67

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