10th Grade Statistics Solution1

In this page 10th grade statistics solution1 we are going to see solution of some practice questions of 10th grade statistics worksheet1.

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

10th grade statistics solution1 10th grade statistics solution1


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