Question

Fifteen randomly selected college students were asked to state the number of hours they slept the previous night. The resulting data are 5, 10, 7, 8, 6, 7, 7, 6, 6, 9, 4, 3, 8, 9, 7. Find the following. (Round your answers to two decimal places.)

(a) Variance s2, using formula below $ s^2 = \dfrac{\sum{(x - \overline{x})^2}}{n - 1}$ s2 =

(b) Variance s2, using formula $ s^2 = \dfrac{\sum{x^2} - \dfrac{(\sum{x})^2}{n}}{n - 1} $ s2 =

(c) Standard deviation, s

Answer 1

Observation table -

x	x^2	(x-x_bar)^2
5	25	3.24
10	100	10.24
7	49	0.04
8	64	1.44
6	36	0.64
7	49	0.04
7	49	0.04
6	36	0.64
6	36	0.64
9	81	4.84
4	16	7.84
3	9	14.44
8	64	1.44
9	81	4.84
7	49	0.04
102	744	50.4

a) -

Variance s², by using the formula - s^2 = \dfrac{\sum{(x - \overline{x})^2}}{n - 1}

From the table, we have -

, , n = 15

So,

Variance is - s² = 3.6.

b) -

Variance s²,using the formula s^2 = \dfrac{\sum{x^2} - \dfrac{(\sum{x})^2}{n}}{n - 1}

From the observation table, we have -

, , n = 14

Variance is - s² = 3.6.

c) -

Standard deviation = = = 1.8974 1.90

standard deviation, s is 1.90.