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yaroslaw [1]
3 years ago
9

HELP ASPAP!!!!! WILL MARK BRAINIEST standard deviation

Mathematics
1 answer:
Umnica [9.8K]3 years ago
5 0

Answer:

The standard deviation of the given data is 11.34.

Step-by-step explanation:

We have to find the standard deviation for the given data;

Grade on     No. of students          

 test (X)        with that score (f)        X \times f       ( X - \bar X)^{2}        f \times ( X - \bar X)^{2}

     50                  1                       50      1073.218      1073.2176

     57                 2                       114      663.578      1327.1552

     60                 4                       240       518.018     2072.0704

     65                 3                       195       315.418      946.2528

     72                 3                       216        115.778       347.3328

     75                12                       900        60.218       722.6112

     77                10                       770        33.178       331.776

     81                 6                       486        3.098       18.5856

     83                 6                       498        0.058        0.3456

     88                9                       792        27.458      247.1184

     90                12                      1080        52.418      629.0112

     92                12                       1104        85.378     1024.5312

     95                 2                        190        149.818      299.6352

     99                 4                        396        263.738     1054.9504

    100          <u>       5   </u>                 <u>    500    </u>     297.218   <u>   1486.088     </u>

   Total             <u>      91       </u>                <u>    7531     </u>                       <u>    11580.68    </u>

Firstly, the mean of the above data is given by;

            Mean, \bar X  =  \frac{\sum X \times f}{\sum f}

                             =  \frac{7531}{91}  =  82.76

Now, the standard deviation of the data is given by;

          Standard deviation, S.D.  =  \sqrt{\frac{\sum f(X-\bar X)^{2} }{\sum f-1}}

                                                     =  \sqrt{\frac{11580.68}{91-1}}

                                                     =  11.34

Hence, the standard deviation of the given data is 11.34.

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