Question

Find the mean and mode for the following data : Classes 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 Frequency 4 8 10 12 10 4 2

Answer 1

mean we can use direct method

first we have to class mark.

10+20/2 =15

20+30/2 =25

30+40/2=35

40+50/2=45

50+60/2=55

60+70/2=65

70+80/2=75

this is Xi.

Now we have to multiply fi and Xi.

15×4=60

25×8=200

35×10=350

45×12=540

55×10=550

65×4=260

75×2=150.

Now add all frequencies=50

add all class Mark's=2110.

Mean= fixi/fi

2110/50

=42.2.

Mean of the data is 42.2.

MODE

In all frequencies highest frequency is 12. so 40-50 is the model class.

Mode=l+(f1-f0/2f1-f0-f2)

In 40-50 lower boundary is 40.

f1= frequency=12

f0=frequency preceding modal class=10

f2= frequency succeeding modal class=10

Mode =40+(12-10/2×12-10-10)

40.5.

mode of the data is 40.5