Find sample standard deviation S.D.

To calculate the sample standard deviation (S.D.) for grouped data, we use the formula:

$$s = \sqrt{\frac{\sum f_i (x_i - \bar{x})^2}{N-1}}$$

where:

• $s$ is the sample standard deviation
• $f_i$ is the frequency of each class
• $x_i$ is the midpoint of each class
• $\bar{x}$ is the sample mean
• $N$ is the total number of observations ($\sum f_i$)

First, we need to determine the midpoints ($x_i$) for each class. Given the classes "700-799" and "800-899", we assume a consistent class width of 100 for the other single-value classes (e.g., "900" means "900-999").

Here is the table with midpoints and calculations:

Class	Frequency ($f_i$)	Midpoint ($x_i$)	$f_i x_i$	$(x_i - \bar{x})$	$(x_i - \bar{x})^2$	$f_i (x_i - \bar{x})^2$
700-799	4	749.5	2998	-500	250000	1000000
800-899	7	849.5	5946.5	-400	160000	1120000
900-999	8	949.5	7596	-300	90000	720000
1000-1099	10	1049.5	10495	-200	40000	400000
1100-1199	12	1149.5	13794	-100	10000	120000
1200-1299	17	1249.5	21241.5	0	0	0
1300-1399	13	1349.5	17543.5	100	10000	130000
1400-1499	10	1449.5	14495	200	40000	400000
1500-1599	9	1549.5	13945.5	300	90000	810000
1600-1699	7	1649.5	11546.5	400	160000	1120000
1700-1799	2	1749.5	3499	500	250000	500000
1800-1899	1	1849.5	1849.5	600	360000	360000
Total	100		124950			6680000