Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If the variance of a data set is 16, and each observation is multiplied by 3, the new standard deviation is
2. The sum of squares of deviations is minimum when taken about
3. The standard deviation of first $n$ natural numbers is
4. Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means?
5. The mean deviation about the mean for the data 6, 7, 10, 12, 13, 4, 8, 12 is
6. Find the mean deviation about the median for the data: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.
7. The mean and variance of 8 observations are 9 and 9.25, respectively. If 6 of the observations are 6, 7, 10, 12, 12, 13, find the remaining two observations.
8. Find the standard deviation for the following data: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
9. Calculate the mean deviation about the mean for the following data:
   Size: 20, 21, 22, 23, 24
   Frequency: 6, 4, 5, 1, 4
10. The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation if the wrong item is omitted.
11. Calculate the mean, variance and standard deviation for the following distribution:
    Class: 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100
    Frequency: 3, 7, 12, 15, 8, 3, 2
12. Case Study: Two plants A and B of a factory show the following results about the number of workers and the wages paid to them.
    Plant A: No. of workers = 5000, Avg monthly wage = Rs 2500, Variance of wages = 81.
    Plant B: No. of workers = 6000, Avg monthly wage = Rs 2500, Variance of wages = 100.
    (i) Which plant pays larger amount as monthly wages?
    (ii) Which plant shows greater variability in individual wages?