Question 1 :

Find the range and coefficient of range of the following data

(i) 59,46,30,23,27,40,52,35,29

Solution:

Definition:

Difference between the largest and smallest terms of the set is called range.

59,46,30,23,27,40,52,35,29

The largest value of the series is 59 and the smallest value is 23

R = L – S

= 59 – 23

= 36

Coefficient of range = (L – S)/(L + S)

= (59 – 23)/(59 + 23)

= 36/82

= 0.4390

= 0.44

(ii) 41.2,33.7,29.1,34.5,25.7,24.8,56.5,12.5

Solution:

Definition:

Difference between the largest and smallest terms of the set is called range.

41.2,33.7,29.1,34.5,25.7,24.8,56.5,12.5

The largest value of the series is 56.5 and the smallest value is 12.5

R = L – S

R = 56.5 – 12.5

= 44

Coefficient of range = (L – S)/(L + S)

= (56.5 – 12.5)/(56.5 + 12.5)

= 44/69

= 0.6376

= 0.64

Question 2:

The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.

Solution:

S = 12     R = 59

R = L – S

59 = L – 12

L = 59 + 12

L = 71

So the largest value is 71.

Question 3:

The largest of 50 measurements is 3.84 kg. If the range  is 0.46 kg ,find the smallest measurement.

Solution:

L = 3.84     R = 0.46

R = L – S

0.46 = 3.84 – S

S = 3.84 – 0.46

S = 3.38 kg

Question 4:

The standard deviation of 20 observations is 5. If each observation is multiplied by 2,find the standard deviation and variance of the resulting observations.

Solution:

Here 5 is the standard deviation of 20 observations. Now we need to find the standard deviation and variance if each observation is multiplied by 2.

Standard deviation (σ) = 2 5

Question 5:

Calculate the standard deviation of the first 13 natural numbers.

Solution:

Formula:

= √(n² -1)/12

= √(13² -1)/12

= √(169 -1)/12

= √168/12

= √14

= 3.7416

= 3.74

Therefore the standard deviation for first 13 numbers is 3.74