Median grouped

9. Procedurę for estimating the median by formuła

The procedurę for estimating the median (by formula) for a grouped freąuency distribution is: STEP X Form a cumulative freąuency (F) column.

STEP 2 Find the value of (where N= £/).

STEP 3 Find that F value that first exceeds, which identifies the median class M.

STEP 4 Calculate the median using the foliowing interpolation formula:

	Median interpolation formula
	Median = Lu +	'*l.f 1 2 fM	^CM
where: LM	= lower bound of the median class
	= cumulative freąuency of class immediately prior to the median class
fu	= actnal freąuency of median class
^CM	= median class width

10. Exampie 3 (The median for a grouped freąuency distribution by formula.)

Question

Estimate the median (using the interpolation formula) for the folio wing data, which represents the ages of a set of 130 representatives who took part in a statistical survey.

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Age in years	20 and under 25	25 and under 30	30 and under 35	35 and under 40	40 and under 45	45 and under 50
Number of representatives	2	14	29	43	33	9

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Answer

STEP 1:

Age (years)	Number of representatives (f)	(F)
20 and under 25	2	2
25 and under 30	14	16
30 and under 35	29	45
35 and under 40	43	88
40 and under 45	33	121
45 and under 50	9	130

iV_ 2 "

STEP 2:

STEP 3: STEP 4:

The median class is the class that has the first F greater than 65. ie 35 to 40. The median can now be estimated using the interpolation formula.

L_m — 35; F_M_₁\ f_M = 43; c_M = 5

Thus, median

⁺

= 35 +

— ~F

Af-1

'M

r

65-45

43

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