10th Grade Statistics Solution5

In this page 10th grade statistics solution5 we are going to see solution of some practice questions of 10th grade statistics worksheet1.

Question 13 :

Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items.

Solution:

Mean of 100 items (x̄) = 48

Standard deviation (σ) = 10

here we have to answer for two questions that is sum of all items (Σ x) and sum of squares all items (Σ x²).

x̄ = (Σ x/n)

48 = (Σ x/100)

Σ x = 100 x 48

     = 4800

Sum of all items = 4800

To find sum of squares of all items, we have to find variance (σ²).

σ² = (Σ x²/n) - (Σ x/n)²

(10)² =  (Σ x²/100) - (4800/100)²

(10)² =  (Σ x²/100) - (48)²

100 = (Σ x²/100) - 2304

100 + 2304 = (Σ x²/100)

2404 = Σ x²/100

Σ x² = 2404 (100)

Σ x² = 240400

Sum of squares of all items = 240400


Question 14 :

The mean and standard deviation of 20 items are found to be 10 and 2 respectively.At the time of checking it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.

Solution:

Mean of 20 items = 10

x̄ = 10

Standard deviation of 20 items = 2

σ = 2

wrong value = 8

correct value = 12

Mean (x̄) = (Σ x/n)

      10 = (Σ x/20)

     10 (20) = Σ x

     Σ x = 200

200 represents sum of 20 items which contain the wrong value. To find the corrected sum we have to use the following method.

corrected  Σ x = 200 - wrong value + correct value

                    = 200 - 8 + 12

                    = 204

Corrected mean (x̄) = (Σ x/n)

                           =  (204/20)

                           = 10.2

Variance (σ²) = (Σ x²/n) - (Σ x/n)²

               4  = (Σ x²/n) - (10)²

               4 = (Σ x²/n) - 100

   4 + 100 = (Σ x²/20)

   104(20) = Σ x²

   Σ x² = 2080

bu this is also wrong Σ x²,to find the corrected Σ x² we have to use this formula

Corrected Σ x²= 2080 - (8)² + (12)²

                    = 2080 - 64 + 144

                    = 2160

Now, let us find corrected variance = (corrected Σx²/n)-corrected (Σ x/n)²

                                                = (2016/20) - (10.2)²

                                                = 108 - 104.04

                                                 = 3.96

           corrected (σ) = √3.96

                              = 1.99

corrected mean = 10.2      

corrected standard deviation = 1.99               

10th grade statistics solution5 10th grade statistics solution5


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