Question

find mean, mode ,median . Variable=4,6,8,10,12. Frequency=4,8,14,11,3

Answer 1

(x)(f) fx
4 4. 16.
6. 8 48
8. 14 112
10. 11. 110
12. 3. 36 total of fx= 322
total full =40
so mean = fx/f
=322/40
=8.05
median is (n+1)/2
=(5+1)/2
=3rd observation I.e 8
mode is the highest frequency I.e 14 3rd observation.

Answer 2

Mean = 8.05

Median = 8

Mode = 8

• CALCULATION OF MEAN:
• Frequency Table

           x            f            fx

           4           4            16

           6           8            48

           8           14           112

           10          11           110

           12           3           36

         TOTAL    40         282

          Mean = $\frac{sum(fx)}{sum(f)}$  

                     = 322/40

                     = 8.05

• CALCULATION OF MEDIAN:

• Given observations as per the given frequency are

        4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12  

         N = 40

         N + 1 = 40 + 1 = 41

         (N+1)/2 = 20.5

         Median = (N+1)/2th observation

                       = 8

• CALCULATION OF MODE:
• Mode = observation with highest frequency

                  = 8