Questions covered in Hard

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. The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. The correct mean is
2. If the coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively, then the difference of their standard deviations is
3. The variance of first $n$ even natural numbers is
4. If $\sum x_i = 180$ and $\sum x_i^2 = 2400$ for 20 observations, then the coefficient of variation is
5. The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.
6. Find the mean deviation about the mean for the data: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
7. 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 if the wrong item is omitted.
8. Prove that the sum of the squares of the deviations of the values of the variable is minimum when taken about their arithmetic mean.
9. Two sets of candidates had means 75 and 60 and standard deviations 10 and 12 respectively. If the first set contained 40 candidates and the combined mean was 70, find the variance of the combined set.
10. Find the coefficient of variation for the following data:
    Class: 0-10, 10-20, 20-30, 30-40, 40-50
    Frequency: 5, 8, 15, 16, 6
11. Calculate the mean deviation about median for the following data:
    Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
    Frequency: 6, 7, 15, 16, 4, 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?
    (iii) Find the combined variance of the wages of all the workers.