Question

If N = 1000, (A) = 700, (B) = 400, (AB) = 50
then the data is​

Answer 1

Explanation:

classes according to the presence or absence of an attribute. ... Thus, in the case of two attributes class-frequencies of order two are ultimate class-frequencies. If A and B are attributes then (AB), (Aβ), (αB), (αβ) are ultimate class-frequencies.

Answer 2

Answer:

If N = 1000, (A) = 700, (B) = 400, (AB) = 50 then the data is​ inconsistent.

Explanation:

Given, N = 1000 , A = 700 ,B = 400 and AB = 50.

As we know that  N = $(A) + (\alpha ) = (B )+ (\beta )$ ........(i)

$(A)= (AB) + (A\beta )$..........(ii)

$(\alpha ) = (\alpha B) +(\alpha \beta )$.........(iii)

$(B) = (AB) + (\alpha \beta )$.....(iv)

and $(\beta ) =(A\beta ) + (\alpha \beta )$....(v)

So, on putting the given values in (i)we get,

N = $(A) + (\alpha ) = (B )+ (\beta )$

⇒1000 = 700+  $\alpha$ = 400$+ (\beta )$

⇒$(\alpha ) =$ 1000 - 700 = 300

and $(\beta )$ = 1000 - 400 = 600.

On putting the given values in (ii)

$(A)= (AB) + (A\beta )$

⇒ 700 = 50 + $(A\beta )$                  [A = 700 and AB = 50 given ]

⇒$(A\beta )$ = 700  - 50 = 650.

On putting the given values in(iv)we get,

$(B) = (AB) + (\alpha \beta )$

400 = 50 + $(\alpha \beta )$                  [where B = 400 and AB = 50 given ]

⇒$(\alpha \beta )$ = 700 -50 = 650

Similarly, on putting the values in (iii) we get,

$(\alpha ) = (\alpha B) +(\alpha \beta )$

⇒300 =  $(\alpha B)$ + 650                [∴$\alpha = 300 and \ \alpha \beta = 650$]

⇒$(\alpha B)$ = 300 -650 = -350

and from (v) we get ,

$(\beta ) =(A\beta ) + (\alpha \beta )$              [ where $\beta =600 and \ \alpha \beta = 650$]

⇒600 = $(A\beta )$ + 650

⇒$(A\beta )$ = 600-650= -50

So here we can see that, the value of $(A\beta ) and \ (\alpha \beta )$ are -50 and -350 which have negative sign.

And we know that, if any frequency is negative then the data is inconsistent otherwise it is consistent.

Hence, the given  data is​ inconsistent.

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