Question

What is the mean and variance of the discrete uniform variate taking values from 1, 2, ...,15?​

Answer 1

Answer:

8

Step-by-step explanation:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

in this mean value is 8

Answer 2

Answer:

mean = 8

variance = 20

Step-by-step explanation:

the values are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

arithmetic mean = sum of all observations/ total number of observations

here, mean = $\frac{1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15}{15}$ =8

therefore, the mean of the given data = 8

x    x-mean    (x-mean)²

1     -7              49

2    -6             36

3    -5              25

4    -4               16

5    -3               9

6     -2              4

7      -1               1

8      0               0

9       1               1

10      2             4

11       3            9

12      4            16

13      5           25

14       6          36

15       7          49

                   ∑(x-mean)² 280

variance S² = ∑(xi- mean)²/ (n-1)

S² is the sample variance

xi is the value of one observation

n = number of observations

S²=$\frac{280}{15-1}$ = $\frac{280}{14}$ = 20

hence, variance of the given data = 20