Question

The marks distribution of 30 students in a mathematics examination are given in the adjacent table. Find the mode of this data. Also compare and interpret the mode and the mean.
Class interval Number of students ( fi) Class Marks (xi ) fixi
10-25 2 17.5 35.0
25-40 3 32.5 97.5
40-55 7 47.5 332.5
55-70 6 62.5 375.0
70-85 6 77.5 465.0
85-100 6 92.5 555.0
Total Σ fi = 30 Σ fixi = 1860.0

Answer 1

Answer:

Mean = 62

Mode = 52

Step-by-step explanation:

Class interval    Number of students ( fi)   Class Marks (xi )     fixi

10-25                    2                                       17.5                        35.0

25-40                   3                                       32.5                         97.5

40-55                   7                                       47.5                         332.5

55-70                   6                                       62.5                         375.0

70-85                   6                                       77.5                         465.0

85-100                   6                                       92.5                         555.0

Total Σ fi = 30                             Σ fixi = 1860.0

Mean = Σ fixi = 1860.0/Σ fi = 30  = 62

Mode lies in 40-55 as 7 is max

Estimated mode =  40  +  (15) (7 - 3)/{(7 -3) + (7-6)}

= 40 + 15 * 4/5

= 40 + 12

= 52

mode < Mean

Answer 2

Step-by-step explanation:

$(f1 - f0 \\ (2f1 - f0 - f2}{?}$

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