For the following frequency distribution, find: (a) the mean, to the nearest whole number. (b) the median. x 10 11 12 13 14 15 16 f 3 2 2 6 3 5 3

The following table gives the duration of movies in minutes: Duration (minutes) Number of movies 100–110 5 110–120 10 120–130 17 130–140 8 140–150 6 150–160 4 Using the step-deviation method, find the mean duration of the movies.

Find the mean of the following frequency distribution using step-deviation method. Take assumed mean = 28. Class interval Frequency 0–8 10 8–16 20 16–24 14 24–32 16 32–40 18 40–48 22

A life insurance agent found the following distribution of ages of 100 policy holders: Age (years) Frequency Cumulative frequency 20–25 2 2 25–30 4 6 30–35 12 18 35–40 20 38 40–45 28 66 45–50 22 88 50–55 8 96 55–60 4 100 On a graph sheet, draw an ogive using the given data. Take 2 cm = 5 years along one axis and 2 cm = 10 policy holders along the other axis. Use your graph to find: (a) the median age. (b) the number of policy holders whose age is above 52 years.

The given graph represents the monthly salaries, in rupees, of workers of a factory. Using the graph, find: (a) the total number of workers. (b) the median class. (c) the lower-quartile class. (d) the number of workers with monthly salary greater than or equal to ₹6,000 but less than ₹10,000.

The given histogram represents the number of plants of different heights grown on a school campus. Study the graph carefully and answer the following questions: (a) Make a frequency table with respect to the class boundaries and their corresponding frequencies. (b) State the modal class. (c) Identify and write the mode of the distribution. (d) Find the number of plants whose height is between 80 cm and 90 cm.

Rakhi’s mobile number has the following integers : 1, 6, 9, 8, 9, 1, 7, 8, 9 The mode of the above given data is : (a) 1 (b) 6 (c) 8 (d) 9

Using a graph paper, draw an ogive for the following distribution which shows a record of weight in kilograms of 100 students. Weight (in kg) Number of students 35–40 4 40–45 6 45–50 10 50–55 24 55–60 26 60–65 17 65–70 8 70–75 5 Use your ogive to estimate the following: (a) the median weight of the students. (b) percentage of students whose weight is 60 kg or more. (c) the weight above which 20% of the students lie.

The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution using the shortcut method. Marks Number of students (f) 0–10 3 10–20 8 20–30 14 30–40 9 40–50 4 50–60 2

The following distribution gives the daily wages of 60 workers of a factory: Daily income (₹) Number of workers 200–300 6 300–400 10 400–500 14 500–600 16 600–700 10 700–800 4 Use graph paper. Take 2 cm = ₹100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the distribution.

Which of the following cannot be determined graphically for a grouped frequency distribution? (a) Median (b) Mode (c) Quartiles (d) Mean

Assertion (A): The mean of the first 9 natural numbers is 4.5. Reason (R): Mean = (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true, and R is the correct reason for A. (d) Both A and R are true, and R is not the correct reason for A.