Question

Consider as SAMPLE data: 52,84,86,91,96,96,98,100,103,105,109.

1) What graph is better - bar graph or histogram?

2) What's sum of squares?

3) What's sample standard deviation?

4) What's sample variance?

Now, consider as POPULATION data: 52,84,86,91,96,96,98,100,103,105,109 (same).

1) What's sum of squares?

2) What's population standard deviation?

3) What's population variance?

Answer 1

(a)

(1)

Bar graph is better

Reason: The given data is raw data. So, bar graph is better. Histogram is for grouped data.

(2)

Sample Mean () is calculated as follows:

From the given data, the following Table is calculated:

x	(x - )	(x - )2
52	- 40.7272	1658.7107
84	- 8.7272	76.1653
86	- 6,7272	45.2562
91	- 1,7272	2.9835
96	3.2727	10.7107
96	3.2727	10.7107
98	5.2727	27.8017
100	7.2727	52.8926
103	10.2727	105.5289
105	12.2727	150.6198
109	16.2727	264.8017
Total =		2406.1818

So,

Sum of Squares = SS is given by:

(3)

Sample Standard Deviation (s) is given by:

(4)

Sample Variance (s²) is given by:

(b)

(1)

Population Mean () is calculated as follows:

From the given data, the following Table is calculated:

x	(x - )	(x - )2
52	- 40.7272	1658.7107
84	- 8.7272	76.1653
86	- 6,7272	45.2562
91	- 1,7272	2.9835
96	3.2727	10.7107
96	3.2727	10.7107
98	5.2727	27.8017
100	7.2727	52.8926
103	10.2727	105.5289
105	12.2727	150.6198
109	16.2727	264.8017
Total =		2406.1818

So,

Sum of Squares = SS is given by:

(2)

Population Standard Deviation () is given by:

(3)

Population Variance (²) is given by: