1Which of the following is standard deviation: a measure of central tendency, the mean, a measure of dispersion, or the median?
2Which is the formula for the coefficient of standard deviation: \( \frac{\bar{X}}{\sigma} \), \( \frac{\sigma}{\bar{X}} \), \( \frac{\sigma}{\bar{X}} \times 100 \) or \( \frac{\sum f|D|}{N} \)?
3If the variance of some data is \( \sigma^2 = 64 \), what is the standard deviation: 8, 16, 32 or 4096?
4Of two data sets, how does the one with the larger coefficient of variation compare with the one with the smaller coefficient of variation: more uniform, less uniform, more varied, or with no variation?
5If \( \sum f(m - \bar{X})^2 = 6400 \) and \( N = 100 \), what is the standard deviation: 10, 64, 32 or 8?
6What is standard deviation? Write it.
7What is the coefficient of variation?
8What is the difference between mean deviation and standard deviation?
9What is the difference between the coefficient of standard deviation and the coefficient of variation?
10If \( N = 100 \), \( \sum fm = 400 \) and \( \sum fm^2 = 4000 \), find the mean and the standard deviation.
11If \( N = 40 \), \( \sum fd = -400 \) and \( \sum fd^2 = 5000 \), where \( d = m - A \) and \( A \) is the assumed mean, find the standard deviation.
12Find the standard deviation and its coefficient. Weight (kg): 10-20, 20-30, 30-40, 40-50, 50-60. Number of students: 5, 10, 12, 7, 6.
13Find the standard deviation and its coefficient. Marks: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70. Number of students: 8, 12, 15, 20, 12, 8.
14Find the standard deviation and its coefficient. Weight (kg): 3-5, 5-7, 7-9, 9-11, 11-13. Number of dogs: 1, 3, 5, 4, 2.
15In a school, 40 students sat a mathematics test of 50 full marks. Marks less than 10, 20, 30, 40, 50: number of students 5, 11, 25, 35, 40. Find the mean marks.
16For the same marks table (less than 10, 20, 30, 40, 50: 5, 11, 25, 35, 40 students), find the standard deviation and its coefficient.
17The daily wages of factory workers range from Rs. 600 to more than Rs. 1200. Workers earning more than Rs. 600, 700, 800, 900, 1000, 1100, 1200 number 100, 80, 55, 25, 15, 8, 4. Find the average wage.
18For the same wage data, find the standard deviation and its coefficient.
19For the same wage data, find the variance.
20For the same wage data, find the coefficient of variation.
21Two shoe factories are compared. Factory A: 40 workers, average monthly salary Rs. 35000, standard deviation Rs. 40. Factory B: 50 workers, average monthly salary Rs. 45000, standard deviation Rs. 35. Which factory spends more on salaries?
22For the same two factories, which one has more uniformity in its salary distribution? Give a reason.
23The marks of 36 class 10 students in mathematics are: 35, 62, 72, 50, 70, 74, 34, 60, 36, 21, 14, 75, 48, 28, 38, 64, 21, 45, 57, 40, 19, 34, 30, 47, 20, 75, 51, 45, 56, 22, 29, 22, 13, 53, 66, 62. Present them in a frequency table whose first class is 10-20.
24From the frequency table of the 36 students, find the average marks.
25From the same table, find the standard deviation and its coefficient.
26From the same table, find the variance and the coefficient of variation.
27Find the standard deviation of the marks in Example 2 (0-10: 3, 10-20: 5, 20-30: 7, 30-40: 3, 40-50: 2) by the step deviation method, and check it against the direct method answer.
28Why does the step deviation formula end with \( \times h \)?
29Group P has mean 20 and standard deviation 5. Group Q has mean 200 and standard deviation 20. Which group is more consistent?