Question

If the ranfe and coefficient of range of the data are 20 and 0.2 respectively. Then find the largest and smallest values of the data​

Answer 1

Answer:

Largest Value = 60

Smallest value = 40

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 20 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                     20   =   L - S

                    L = 20 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                         0.2   =  $\frac{L-S}{L+S}$  

                                        0.2 = $\frac{20}{L+S}$

                   L + S = 20/0.2 = 100

So,    L + S = 100

         20 + S + S = 100   {using equation 1}

             2*S = 80

               S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

                 smallest value, S = 40

                           

Answer 2

Answer:

Range= 20

coefficient of range = 0.2

we know that,

range = L-S &

coefficient of range = L-S/L+S

let we take range first, then

range = L+S

20 = L+S

L= 20+s ...........(1)

now let we take coefficient of range ,then,

c.of.range = 0.2

L-S/L+S = 0.2........(2)

20/L+ S = 0.2

L +S = 20/0.2

= 20/0.2 × 10/10

L + S = 100 ..............(3)

from (1) & (3), sub L = 20+ S in (3)

hence we get,

20 + S + S = 100

20 + 2S = 100

2S = 100 - 20

2 S = 80

S = 80/2

S = 40.........(4)

sub S = 40 in (1)

L = 20+S

= 20 + 40

L = 60.............(5)

• therefore, Smallest value = 40

Largest value = 60