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.

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.

Use graph paper to answer this question. During a medical check-up of 60 students in a school, their weights were recorded as follows: Weight (kg) Number of students 28–30 2 30–32 4 32–34 10 34–36 13 36–38 15 38–40 9 40–42 5 42–44 2 Taking 2 cm = 2 kg along one axis and 2 cm = 10 students along the other axis, draw an ogive. Use the graph to find: (a) the median (b) the upper quartile (c) the number of students whose weight is above 37 kg.

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 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.

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.

For the following frequency distribution, find:(a) the mean, to the nearest whole number.(b) the median.x10111213141516f3226353

Assertion (A): A die is thrown once and the probability of getting an even number is 2/3. Reason (R): The sample space for even numbers on a die is {2, 4, 6}. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true. (d) Both A and R are false.

The sum invested to purchase 15 shares of nominal value ₹75 each at a discount of 20% is: (a) ₹60 (b) ₹90 (c) ₹1350 (d) ₹900

The 7th term of the A.P. is: (a) (b) (c) (d)