Statistics quiz

The class mark of the class 20-30 is:

The class having the maximum frequency is called the:

In the formula mean = a + (sum fu / sum f) x h for the step-deviation method, u is:

The measure of central tendency that is found using cumulative frequencies is the:

If mode = 24 and mean = 30, then by the empirical relation the median is:

The modal class of the distribution 0-10: 3, 10-20: 9, 20-30: 15, 30-40: 30, 40-50: 18 is:

For grouped data, the mean is computed on the assumption that the frequency of each class is:

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

For the data 0-10: 6, 10-20: 9, 20-30: 15, 30-40: 12, 40-50: 8, the median class is:

Which measure of central tendency is best for finding the most popular shirt size sold in a shop?

Find the class marks of the classes 15-25, 25-35 and 35-45, and the class size. (2 marks)

Write two situations where the median is a more suitable measure than the mean. (2 marks)

Explain the assumed mean method and why it reduces calculation. (2 marks)

If the mean and median of a distribution are 26.4 and 26.67 respectively, find the mode using the empirical relation. (2 marks)

Find the modal class and the median class of: 0-5: 6, 5-10: 10, 10-15: 14, 15-20: 12, 20-25: 8. (2 marks)

What is the difference between a less than type and a more than type cumulative frequency distribution? (2 marks)

The marks of 40 students give sum fx = 1540 with all class marks used. Find the mean marks. (2 marks)

Why is the modal class not necessarily the class with the largest class mark? Explain with an example. (2 marks)

Convert the following into a frequency distribution: less than 10: 5, less than 20: 13, less than 30: 28, less than 40: 44, less than 50: 50. (2 marks)

In the step-deviation method, with a = 150 and h = 20, a class mark of 190 gives what value of u? A class mark of 110? (2 marks)

The daily wages of 50 workers of a factory are: 100-120: 12, 120-140: 14, 140-160: 8, 160-180: 6, 180-200: 10 (wages in rupees). Find the mean daily wage using the assumed mean method. (3 marks)

The following table shows the monthly consumption of electricity of 68 consumers of a locality: 65-85: 4, 85-105: 5, 105-125: 13, 125-145: 20, 145-165: 14, 165-185: 8, 185-205: 4 (units). Find the median of the data. (3 marks)

Find the mode of the electricity consumption data in Q22 and compare it with the median. (3 marks)

The marks obtained by 50 students in a test are: 20-25: 3, 25-30: 5, 30-35: 9, 35-40: 12, 40-45: 11, 45-50: 6, 50-55: 4. Find the mean using the step-deviation method. (3 marks)

For the marks data in Q24, find the median and the mode, and verify the empirical relation approximately. (3 marks)

Read the passage and answer the questions. A school health survey recorded the weights of 50 students: 50-60 kg: 8, 60-70 kg: 12, 70-80 kg: 20, 80-90 kg: 6, 90-100 kg: 4. (Here the classes are 50-60, 60-70 and so on.) (i) Find the class marks and the modal class. (ii) Find the mean weight by the direct method. (iii) Find the median weight. (5 marks)

Read the passage and answer the questions. A mobile store records the number of phones sold per day for 50 days: 0-10: 6, 10-20: 9, 20-30: 15, 30-40: 12, 40-50: 8. (i) Find the modal class and the mode. (ii) Find the median number of phones sold. (iii) The manager wants to plan stock for a typical day. Which measure should she use and why? (5 marks)

Read the passage and answer the questions. A teacher records the time (in minutes) taken by 40 students to solve a puzzle: 10-20: 4, 20-30: 6, 30-40: 10, 40-50: 12, 50-60: 8. (i) Prepare the less than cumulative frequency table. (ii) Find the median time. (iii) Find the mode and state what it tells the teacher. (5 marks)

Read the passage and answer the questions. A village survey records the daily income of 100 families: 0-20: 10, 20-40: 15, 40-60: 25, 60-80: 30, 80-100: 20 (income in hundreds of rupees). (i) Find the mean daily income. (ii) Find the median income. (iii) Find the modal income and comment on which measure best represents a typical family. (5 marks)

Read the passage and answer the questions. A hospital records the ages of 60 patients admitted in a month: 0-10: 5, 10-20: 8, 20-30: 20, 30-40: 15, 40-50: 7, 50-60: 5. (i) Find the median class. (ii) Find the median age. (iii) Find the mean age. (5 marks)

Explain the direct, assumed mean and step-deviation methods for finding the mean of grouped data. Use all three methods to find the mean of: 100-120: 4, 120-140: 6, 140-160: 10, 160-180: 12, 180-200: 8, and show that they give the same answer. Draw a histogram of the data. (6 marks)

Derive the meaning of each term in the mode formula l + ((f1 - f0)/(2f1 - f0 - f2)) x h with the help of a histogram of the modal class and its neighbours. Find the mode of: 0-20: 10, 20-40: 15, 40-60: 25, 60-80: 30, 80-100: 20. (6 marks)

The following distribution gives the marks of 50 students: 0-10: 5, 10-20: 8, 20-30: 15, 30-40: 16, 40-50: 6. Find the mean, median and mode. Draw a histogram and a frequency polygon on the same graph. (6 marks)

A life-time test of 400 neon lamps gave: 1500-2000: 14, 2000-2500: 56, 2500-3000: 60, 3000-3500: 86, 3500-4000: 74, 4000-4500: 62, 4500-5000: 48 (hours). Find the median life of a lamp and the modal life. Draw a bar diagram of the frequencies. (6 marks)

The median of the distribution 0-10: 5, 10-20: x, 20-30: 20, 30-40: 15, 40-50: y, 50-60: 5 is 28.5, and the total frequency is 60. Find x and y. Then find the mean of the completed distribution and the mode, and check the empirical relation. (6 marks)