Find arithmetic mean and standard deviation from the following data. Also find coefficient of Variation. (AKTU 2017) Age (Less than) 10 20 30 40 50 60 70 80 No. of persons 15 30 50... Find arithmetic mean and standard deviation from the following data. Also find coefficient of Variation. (AKTU 2017) Age (Less than) 10 20 30 40 50 60 70 80 No. of persons 15 30 50 75 100 110 115 125 Find the Standard Deviation of the following data: (AKTU-2018) Age (in years) 4-6 6-8 8-10 10-12 12-14 14-16 16-18 No. of students 30 90 120 150 80 60 20 From the following data compute Standard Deviation and Coefficient of Variation: (AKTU 2017) Marks 0-10 10-20 20-30 30-40 40-50 No. of Students 6 10 20 9 5 From the prices of shares of X and Y below find out which is more stable in value. (AKTU 2018) X 53 54 52 53 56 58 52 50 51 Y 108 107 105 106 107 104 103 104 Monthly Wages (in '000 Rs.) 2-3 3-4 4-5 5-6 6-7 7-8 8-9 No. of workers Factory A 15 30 40 60 30 14 7 Factory B 25 40 60 35 20 15 5 In which factory are wages more uniform? (AKTU 2017) The following table gives the frequency distribution of expenditure on education per family among middle class families in two cities. (AKTU 2016) Expenditure (in thousand Rs.) No. of Families City 'A' 3-6 28 39 6-9 292 284 9-12 389 404 12-15 212 202 15-18 59 48 18-21 18 21 21-24 2 5 a) Find the standard deviation of the expenditure at both cities. b) Find out which of the city shows greater variability. Goals scored by two teams in a football session are as follows. Which team is more consistent in its game? (AKTU 2023-24) No of Goals Scored in a football match A B No. of football matches played 0 15 20 1 10 10 2 7 5 3 5 4 4 3 2 5 2 1 Read more

Steps to Solve

1. Calculate Mean and Standard Deviation for Data (AKTU 2017)

   For the age distribution, calculate the mean ($\mu$) using the formula: $$ \mu = \frac{\sum (x \cdot f)}{N} $$ where $x$ is the midpoint of age groups and $f$ is the frequency (No. of persons), and $N$ is the total frequency.

   Then, use the standard deviation formula: $$ \sigma = \sqrt{\frac{\sum f(x - \mu)^2}{N}} $$

2. Calculate Coefficient of Variation

   The coefficient of variation (CV) is given by: $$ CV = \frac{\sigma}{\mu} \times 100 $$ Use the calculated mean and standard deviation to find the CV.

3. Calculate Standard Deviation for Data (AKTU 2018)

   Follow the same steps with age data provided in question 6, using: $$ \sigma = \sqrt{\frac{\sum f(x - \mu)^2}{N}} $$

4. Compute Standard Deviation and Coefficient of Variation from Marks Data (AKTU 2017)

   Similar to earlier steps, use the provided marks data to find mean, standard deviation, and then CV.

5. Analyze Stability of Shares from Data (AKTU 2018)

   For shares X and Y, calculate standard deviation to determine stability. The share with a lower standard deviation is more stable.

6. Calculate Uniformity of Wages (Factory A and B)

   For the sample data on monthly wages, calculate standard deviation for both factories using: $$ \sigma = \sqrt{\frac{\sum f(x - \mu)^2}{N}} $$ The factory with the lower standard deviation indicates more uniform wages.

7. Find Standard Deviations of Expenditure Data for Cities A and B (AKTU 2016)

   Use the standard deviation formula for each city's expenditures, then compare the two standard deviations to find which city shows greater variability.

8. Determine Consistency of Teams from Football Match Data (AKTU 2023-24)

   Using the goals scored data, calculate the mean and standard deviation for both teams A and B. The team with a lower standard deviation is more consistent.