Question

Compute the A.M., G.M., & H.M. from the following: Class 15-19 20-24 25-29 30-34 35-39 40-44 Frequency 13 32 4 42 58 51

Answer 1

Answer:

Compute the A.M., G.M., & H.M. from the following: Class 15-19 20-24 25-29 30-34 35-39 40-44 Frequency 13 32 4 42 58 51

Step-by-step explanation:

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Answer 2

A.M is 33.345, G.M is 32.224 and H.M is 29.04

Given

Class 15-19 20-24 25-29 30-34 35-39 40-44

Frequency 13 32 4 42 58 51

To Find

A.M, G.M, and H.M

Solution

Here we can see that

the class are discontinuous.

Hence we will first convert them into continuous classes.

To convert to continuous classes we will use the formula

new lower limit = (Lower limit of current class + upper limit of previous class)/2

and,

new upper limit = (upper limit of current class + lower limit of next class)/2

This way we get 14.4-19.5, 19.5-24.5... and so on

Now we will find the class mark.

Classmark = (lower limit + upper limit)/2

Hence

class mark of 14.5-19.5 = (14.5 + 19.5)/2 = 34/2

= 17.

class mark of 19.5-24.5 = (19.5 + 24.5)/2 = 44/2

= 22.

and so on...

After this, we will multiply the value of the class mark by the frequency of the corresponding class

This way we get the table as follows

$\begin{tabular}{ c c c c c }class & contimuous class & class mark(x) & frequency(f) & xf\\ 15-19 & 14.5-19.5 & 17 & 13 & 221 \\ 20-24 & 19.5-24.5 & 22 & 32 & 704\\ 15-29\ & 24.5-29.5&27 & 4 & 112\\ 30-34 & 29.5-34.5 &32 & 42 & 1344\\ 35-39 & 34.5-39.5& 37& 58 & 2146 \\40-44 & 39.5-44.5&42 &51 & 2142\\\end{tabular}$

Here,  N ∑f = 200

A.M or Arithmetic mean = ∑xf/N

∑xf = 221 + 704 + ... + 2142

= 6669

Therefore,

Arithmetic mean

= 6669/200

= 33.345

Geometric mean = ⁿ√(πx^f)

= ⁿ√(x^f₁) (x₂^f) (x₃f₃)₃....(xn^fn)

= ²⁰⁰√17^13 X 22^32 X ... X42^51

=     32.224

Harmonic mean = N/∑(f/x)

= 200/((13/17) + 32/22 + ... + 51/42)

= 29.04

Therefore, A.M is 33.345, G.M is 32.224 and H.M is 29.04

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