Statistics quiz

The standard deviation of 5, 5, 5, 5 is:

Variance is equal to:

The range of 3, 8, 1, 10 is:

If every observation is increased by k, the standard deviation:

The mean deviation about the mean of 1, 2, 3 is:

The variance of 1, 2, 3, 4, 5 is:

The mean deviation is least when taken about the:

If every observation is multiplied by 2, the standard deviation is:

The sum of the deviations of observations from their mean is:

The standard deviation is:

Define variance and standard deviation. (2 marks)

Why are absolute values of deviations used in mean deviation? (2 marks)

Write the shortcut formula for variance. (2 marks)

Find the mean deviation about the mean of 40, 50, 60, 70, 80. (2 marks)

The mean of 5 observations is 4.4. Find their sum. (2 marks)

Explain why the standard deviation is unaffected by a change of origin. (2 marks)

What is a class mark? How is it used for a continuous distribution? (2 marks)

Find the variance of 30, 32, 28, 31, 29. (2 marks)

State two limitations of the range as a measure of dispersion. (2 marks)

Explain the step-deviation method for finding variance. (2 marks)

The mean and variance of 5 observations are 4.4 and 8.24. If three of them are 1, 2 and 6, find the other two. (3 marks)

Find the mean deviation about the mean for classes 0-10, 10-20, 20-30, 30-40, 40-50 with frequencies 5, 8, 15, 16, 6. (3 marks)

Find the standard deviation of 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. (3 marks)

Find the variance of the wages Rs 100, 200 and 300 with frequencies 2, 5 and 3. (3 marks)

The mean of 10 observations is 12 and their variance is 9. Find the sum of their squares. (3 marks)

Read the passage and answer the questions. The maximum temperatures in a city on five days were 30, 32, 28, 31 and 29 degrees Celsius. (i) Find the mean. (ii) Find the variance. (iii) Find the range and the standard deviation. (5 marks)

Read the passage and answer the questions. Five students scored 40, 50, 60, 70 and 80 marks. (i) Find the mean deviation about the mean. (ii) Find the variance and standard deviation. (iii) If every student gets 5 grace marks, find the new mean and standard deviation. (5 marks)

Read the passage and answer the questions. A machine produces bolts. Four bolts measured 9.8, 10.0, 10.2 and 10.0 mm. (i) Find the mean length. (ii) Find the variance. (iii) Find the standard deviation. (5 marks)

Read the passage and answer the questions. Workers in a small unit earn Rs 100, 200 or 300 a day. The numbers of workers are 2, 5 and 3. (i) Find the mean wage. (ii) Find the variance. (iii) Find the standard deviation. (5 marks)

Read the passage and answer the questions. A teacher has a set of 5 marks with mean 4.4 and variance 8.24. (i) Find the sum of the marks. (ii) Find the sum of their squares. (iii) If three marks are 1, 2 and 6, find the other two. (5 marks)

Explain the need for measures of dispersion. Compare range, mean deviation and standard deviation as measures of spread. (6 marks)

Describe how to find the mean deviation about the median for a continuous frequency distribution, with an example of your choice. (6 marks)

Derive the shortcut formula variance = (sum of x^2)/n - (mean)^2 from the definition of variance. (6 marks)

Show that if each observation is multiplied by a constant a, the variance is multiplied by a^2, and if a constant b is added, the variance does not change. (6 marks)

Find the mean and standard deviation of the first n natural numbers, and verify your result for n = 5. (6 marks)