Question

Calculate the mean for the following frequency distribution?
Height: 150-160 160-170 170-180 180-190
No. of students: 15 25 18 2​

Answer 1

Answer:

Here:

Maximum class frequency =20

The class corresponding to Maximum class frequency is the modal class.

So, Modal class =160−165

Lower limit =L=160

Modal class size =h=5

Frequency of class preceding the modal class =f0=8

Frequency of the modal class =f1=20

Frequency of class succeeding the modal =f2=12

Mode formula is given by,

Mode =L+(

2f

1

−f

0

−f

2

f

1

−f

0

)×h

Mode =160+(

2(20)−8−12

20−8

)×12

=160+12/20×5

=163

The modal height is 163 cm, which implies maximum number of students have model height 163 cm

Height Mid Point (x

i

) No. of students (f

i

) f

i

x

i

150−155

152.5 15 2287.5

155−160 157.5 8 1260

160−165 162.5 20 3250

165−170 167.5 12 2010

170−175 172.5 5 862.5

∑fi=60 ∑fixi=9670

We know,

x

ˉ

=

∑

i

f

1

∑

i

f

i

x

i

=9670/60

=161.17

Mean is 161.17

Thus, 161.7 cm is the average height of all the students.

Step-by-step explanation:

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