Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Define the term "mean" of a data set. Mean is the of all observations, calculated by dividing the of all observations by the of observations

Perfect! Mean = Sum of observationsNumber of observations.

(2) What is the formula for calculating the median of a grouped data? Median = l + n2−CFf × h, where l = lower boundary of class, CF = frequency before median class, f = of median class, h = class

Excellent! This is the standard median formula for grouped data.

(3) What is the class mark of a class interval 20–30? Class mark =

Perfect! Class mark is the midpoint of the class interval.

(4) Find the class width of the class 40–50. Class width =

Correct! Class width is the difference between upper and lower limits.

(5) State the formula for mode using the empirical relation between mean, median, and mode. Mode = × -+ ×

Excellent! This is the empirical relationship for moderately skewed data.

Short Answer Questions (2 Marks Each)

(1) The marks obtained by 5 students in a test are: 10, 15, 20, 25, 30. Find the mean. Mean =

Perfect! The mean marks is 20.

(2) Find the median of the following data: 5, 10, 15, 20, 25 Median =

Excellent! For odd number of observations, median is the middle value.

(3) Calculate the class mark for the class interval 60–70. Class mark =

Perfect! Class mark represents the center of the class interval.

(4) If the mean of 6 numbers is 12, find the sum of all numbers. Sum =

Excellent! Used the mean formula to find the sum.

(5) The mode of the data 2, 3, 3, 5, 6 is: Mode =

Perfect! Mode is the most frequently occurring value.

(6) Write any one advantage of using mean in statistics.

Long Answer Questions (4 Marks Each)

(1) Find the mean of the following data using the direct method: Class intervals: 0–10 (5), 10–20 (8), 20–30 (15), 30–40 (7), 40–50 (5). Mean = (upto two decimal places)

Excellent! Systematic application of the direct method.

(2) The following table shows the marks obtained by 40 students in a test. Calculate the median: Marks: 0–10 (5), 10–20 (8), 20–30 (12), 30–40 (10), 40–50 (5). Median = (upto two decimal places)

Perfect! Median ≈ 25.83 marks.

(3) Find the mode of the following data using the formula: Class intervals: 10–20 (6), 20–30 (8), 30–40 (12), 40–50 (5), 50–60 (3). Mode = (upto two decimal places)

Excellent! Mode ≈ 33.64 using the standard formula.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The average of the numbers 2, 4, 6, 8, 10 is:

(a) 5 (b) 6 (c) 7 (d) 8

Correct! Average = 2+4+6+8+105 = 305 = 6.

(2) The median of 3, 5, 7 is:

(a) 4 (b) 5 (c) 6 (d) 7

Correct! For 3 values, median is the middle value = 5.

(3) The mode of the data 2, 3, 4, 4, 5 is:

(a) 2 (b) 3 (c) 4 (d) 5

Correct! 4 appears twice, more than any other value.

(4) Class width of the class interval 10–20 is:

(a) 10 (b) 15 (c) 5 (d) 20

Correct! Class width = Upper limit - Lower limit = 20 - 10 = 10.

(5) Class mark of the class 30–40 is:

(a) 30 (b) 35 (c) 40 (d) 25

Correct! Class mark = 30+402 = 35.

(6) The sum of the observations divided by the number of observations gives the:

(a) Mode (b) Median (c) Mean (d) Range

Correct! This is the definition of arithmetic mean.

(7) The median is the value of the:

(a) Most frequent observation (b) Middle observation (c) Least observation (d) Average of data

Correct! Median is the middle value when data is arranged in order.

(8) In a frequency distribution, the class having the highest frequency is called:

(a) Modal class (b) Median class (c) Upper class (d) Lower class

Correct! Modal class contains the mode and has the highest frequency.

(9) The mean is affected by:

(a) Extreme values (b) Median (c) Mode (d) None

Correct! Mean is sensitive to outliers and extreme values.

(10) A bar graph is used to represent:

(a) Qualitative data (b) Ungrouped data (c) Grouped data (d) All types of data

Correct! Bar graphs are typically used for ungrouped (discrete) data.

Basic Statistics Challenge

Determine whether these statements about basic statistics are True or False:

Basic Statistics Quiz

🎉 You Did It! What You've Learned:

By completing this worksheet, you now have a solid understanding of:

(1) Basic Definitions: Clear understanding of mean, median, and mode

(2) Simple Calculations: Finding measures of central tendency for ungrouped data

(3) Class Concepts: Class mark, class width, and their calculations

(4) Direct Method: Step-by-step calculation of mean for grouped data

(5) Median Formula: Understanding and applying median formula for grouped data

(6) Mode Formula: Finding mode using the standard statistical formula

(7) Practical Applications: Solving real-world problems using statistical measures

(8) Foundation Skills: Building blocks for advanced statistical analysis

Excellent work building a strong foundation in basic statistical concepts!