Question

The mean of two samples of sizes 200 and 300 were found to be 25 and 10 respectively.
Find their mean and SD of combined distribution.

Pleaseee helpp. It's urgent

Answer 1

Mean is 14.285
Combined distribution is 8000

Answer 2

Mean is 16, Standard deviation is 7.35.

Step-by-step explanation:

1. From Table

$X_{i}$          $F_{i}$             $X_{i}F_{i}$              $F_{i}(X_{i}-\bar{X})^{2}$  

 25          200      25×200      $200\times (25-16)^{2}=16200$

 10           300      10×300       $300\times (10-16)^{2}=10800$

              =500      =8000          = 27000

2. Where

  $\sum F_{i}=500$  

  $\sum F_{i}X_{i}=8000$

  $\sum F_{i}(X_{i}-\bar{X})^{2}=27000$

3. Mean

   $\bar{X}=\frac{\sum F_{i}X_{i}}{\sum F_{i}}=\frac{8000}{500}=16$

4. Variance

  $\sigma ^{2}=\frac{\sum F_{i}(X_{i}-\bar{X})^{2}}{\sum F_{i}}=\frac{27000}{500}=54$

     

5. Standard deviation (SD)

   $SD=\sqrt{variance}=\sqrt{\sigma ^{2}}= \sqrt{54}=7.35$