Question

find the mean deviation about mean and median.
32,33,32,43,46,48,50,36,39,49,42​ ?

Answer 1

Answer:

The mean deviation about mean is 5.91.

The mean deviation about median is 5.81.

Step-by-step explanation:

Arranging the given data in ascending order:  

32, 32, 33, 36, 39, 42, 43, 46, 48, 49, 50 ……………(i)

No. of observation, N = 11 (odd)

We have to find the mean deviation (M.D.) about the mean and median.

Mean deviation about the mean:

Mean, X = ( ∑xi )/ N

             = (32+32+33+36+39+42+43+46+48+49+50) / 11  

              = 450/11  

               = 40.9

Mean deviation, M.D. = ( ∑ | xi - X | ) / N

Now we will calculate for |  xi - X  |

∴ |32 - 40.9| = 8.9

|32 - 40.9| = 8.9

|33 – 40.9| = 7.9

|36 - 40.9| = 4.9

|39 - 40.9| = 1.9

|42 – 40.9| = 1.1

|43 – 40.9| = 2.1

|46 – 40.9| = 5.1

|48 – 40.9| = 7.1

|49 – 40.9| = 8.1

|50 – 40.9| = 9.1

∴ M.D. = (8.9+8.9+7.9+4.9+1.9+1.1+2.1+5.1+7.1+8.1+9.1) / 11

            = 65.1 / 11

            = 5.91

Mean deviation about the median:

Since n is odd here

∴ Median, M = {(11+1) / 2}th observation  

                    = (12/2)th observation

                    = 6th observation

                     = 42……………. [ from equation (i)]

Mean deviation, M.D. = ( ∑ | xi - M | ) / N

Now we will calculate for | xi - M |

∴|32 - 42| = 10

|32 - 42| = 10

|33 – 42| = 9

|36 - 42| = 6

|39 - 42| = 3

|42 – 42| = 0

|43 – 42| = 1

|46 – 42| = 4

|48 – 42| = 6

|49 – 42| = 7

|50 – 42| = 8

∴ M.D. = (10+10+9+6+3+0+1+4+6+7+8) / 11

           = 64 / 11

           = 5.81