Question

On the sports day of a school, 300 students participated. Their ages are given in
distribution
Age (in years) 5-7 7-9 9-11 .11 -13 13-15 15 - 17 | 1710
Number of students 67 33 41 95 3 6 13 15
Find the mean and mode of the data.​

Answer 1

Step-by-step explanation:

Given On the sports day of a school, 300 students participated. Their ages are given in  distribution

Age (in years) 5-7 7-9 9-11 .11 -13 13-15 15 - 17 | 1710

Number of students 67 33 41 95 3 6 13 15

Find the mean and mode of the data.

So l = 11, f1 = 95, fo = 41, f2 = 36, h = 2

Mode = l + f1 – fo / 2f1 – fo – f2 x h

         = 11 + 95 – 41 / 190 – 41 – 36 x 2

         = 11 + 54 / 113 x 2

So Mode = 11 + 0.95

               = 11.95

Age        xi          fi         fixi

5 – 7       6          67         402

7 -9         8          33         264

9 – 11     10         41        410

11 – 13    12        95       1140

13 – 15    14        36         504

15 – 17     16       13         208

17 – 19      18       15        270

         So ∑ fi = 300 and  ∑fixi = 3,198

Now Mean x bar = ∑ fixi / ∑ fi

                           = 3198 / 300

                           = 10.66