Quantiles

11 Ouantiles and the ąuartite dewation r-

Expenditure (£)	Number of companies
Less than 500	210
500 and up to 1000>	184
1000 and up to 1500	232
1500 and up to 2000	348
2000 and up to 2500	177
2500 and up to 3000	83
3000 and up to 3500	48
3500 and up to 4000	12
4000 and over	9

c

Table 1

O

Table 2

—		>1
Upper bound	F	F%
500	210	16.1
1000	394	30.2
1500	626	48.0
2000	974	74.8
2500	1151	88.3
3000	1234	94.7
3500	1282	98.4
4000	1294	99.3
^5000*	1303	100
Nominał upper bound
V_		J

■ r..L"

100 -l

Eercentage

Cumulative frequency curve of companies advertising expenditure

Expenditure (£)

“i

6000

r

4000

T

5000

(ED

13. General interpolation formula for quantiłes

a)    There are two methods of estimating the median value of a grouped freąuency distribution; the graphic|&£ and interpolation methods, although it should be noted that the graphical method is generally preferred. The median interpolation formuła can be generalized to include the other two ąuartiles (and indeed anynf the other quantiles described in foliowing sections).

b)    The generalized interpolation formula to estimate the value of some defined ąuantile, Q, is given as follc

Formula for a ąuantile

~^Fq-i

Q - L₀ +

f,

where:

Lq = lower bound of the ąuantile class P_Q = position of ąuantile in distribution

= cumulative freąuency of class irńmediately prior to the ąuantile class f_Q = actual freąuency of ąuantile class Cq = ąuantile class width