Hard Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Define cumulative frequency. Running total of frequenciesTotal sum of frequencies

Correct! Cumulative frequency is the running total of frequencies up to a particular class or value.

(2) Find the median of the data: 3, 7, 8, 12, 15, 18.

Perfect! For 6 values, median = (8 + 12) ÷ 2 = 10.

(3) Find the mode of the data: 5, 7, 7, 9, 9, 9, 12.

Excellent! 9 appears three times, making it the mode.

(4) Find the mean of the data: 12, 15, 18, 20, 25.

Great! Mean = (12+15+18+20+25) ÷ 5 = 90 ÷ 5 = 18.

(5) Find the range of the data: 6, 8, 12, 14, 18, 20.

Correct! Range = 20 - 6 = 14.

Short Answer Questions (2 Marks Each)

Answer each question with detailed calculations

(1) The marks obtained by 12 students are: 18, 15, 10, 12, 22, 14, 15, 16, 18, 12, 20, 20, . Find the mean and mode.

Mean: Mode: 12,15,18,2015,18,20

Excellent! Mean = 194 ÷ 12 ≈ 16.17, Mode = 12, 15, 18, 20 (each appears twice).

(2) Construct a frequency table for the marks: 5, 7, 7, 8, 8, 8, 9, 10, 10, 10, 11, 12, 12, 12, 13.

(3) Find the median of the data: 8, 12, 14, 16, 18, 20, 22, 24, 26.

Median:

Perfect! The median is the 5th value: 18.

(4) Find the mean marks from the grouped data.

Mean:

Correct! Using midpoints: Mean = (5×3 + 15.5×7 + 25.5×6 + 35.5×4) ÷ 20 = 400 ÷ 20 = 20.

(5) The daily sales are: 12, 14, 14, 16, 16, 16, 18, 18, 20, 22. Find the mode and range.

Mode: Range:

Great! Mode = 16 (appears 3 times), Range = 22 - 12 = 10.

Long Answer Questions (4 Marks Each)

(1) For the 25 student marks, construct a cumulative frequency table and find the median.

Median:

Correct! For 25 values, median is the 13th value. From cumulative frequency, the 13th value is 18.

(2) Calculate mean and median from grouped data.

Mean: Median:

Perfect! Mean = (5×4 + 15.5×6 + 25.5×8 + 35.5×10 + 45.5×2) ÷ 30 = 780 ÷ 30 = 26. Median class is 31-40.

(3) Create frequency table for heights and find mean.

Mean height: cm

Excellent! Using midpoints: Mean = (142×3 + 147×5 + 152×5 + 157×5 + 162×2) ÷ 20 = 3030 ÷ 20 = 151.5 cm.

(4) Find mean marks in each subject and determine which has higher average.

Mean Maths: Mean Science: Higher average:

Great! Maths mean = 262 ÷ 15 ≈ 17.47, Science mean = 266 ÷ 15 ≈ 17.73. Science has higher average.

(5) Find the median production from grouped data.

Median production: units

Correct! Total = 20, median position = 10th and 11th values. Median class is 51-100. Using formula: Median ≈ 87.5 units.

Part B: Objective Questions (1 Mark Each)

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

(1) The mean of 5, 10, 15, 20, 25 is:

(a) 10 (b) 15 (c) 20 (d) 25

Correct! Mean = (5+10+15+20+25) ÷ 5 = 75 ÷ 5 = 15.

(2) The median of 7, 9, 11, 13, 15, 17 is:

(a) 11 (b) 12 (c) 13 (d) 14

Correct! For 6 values, median = (11 + 13) ÷ 2 = 12.

(3) The mode of 2, 3, 3, 4, 5, 5, 5, 6, 7 is:

(a) 3 (b) 4 (c) 5 (d) 6

Correct! 5 appears three times, which is the highest frequency.

(4) The range of 12, 15, 18, 20, 22 is:

(a) 10 (b) 8 (c) 12 (d) 14

Correct! Range = 22 - 12 = 10.

(5) Cumulative frequency helps in finding:

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

Correct! Cumulative frequency is primarily used to find the median and percentiles.

(6) If all values in a data set are increased by 5, the mean:

(a) Increases by 5 (b) Decreases by 5 (c) Remains same (d) Cannot be determined

Correct! When a constant is added to all values, the mean increases by that constant.

(7) The median class is:

(a) The class containing the mode (b) The class containing the median (c) The class with highest frequency (d) The class with lowest frequency

Correct! The median class is the class interval that contains the median value.

(8) The sum of observations is 240 and the number of observations is 12. The mean is:

(a) 10 (b) 15 (c) 20 (d) 25

Correct! Mean = Sum ÷ Number = 240 ÷ 12 = 20.

(9) For the data 4, 4, 5, 5, 5, 6, 6, 7, the mode is:

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

Correct! 5 appears three times, which is the highest frequency.

(10) The range of data 18, 22, 24, 30, 36 is:

(a) 12 (b) 14 (c) 16 (d) 18

Correct! Range = 36 - 18 = 18.

Expert Statistics Challenge

Determine whether these statements are True or False:

Expert Statistics Mastery Quiz

🎉 Congratulations! What You've Mastered:

You have successfully completed Statistics worksheet and learned:

(1) Cumulative Frequency Analysis: Understanding and constructing cumulative frequency tables for complex datasets

(2) Advanced Grouped Data Techniques: Working with class intervals and calculating statistics from grouped data using midpoint methods

(3) Median Class Identification: Locating and working with median classes in large grouped datasets

(4) Multi-subject Statistical Comparison: Analyzing and comparing statistical measures across different subjects or categories

(5) Large Dataset Management: Organizing and analyzing datasets with 20+ observations systematically

(6) Professional Data Applications: Working with real-world scenarios like production data, test scores, and industrial measurements

(7) Advanced Statistical Properties: Understanding how transformations affect different measures of central tendency

(8) Complex Frequency Distribution: Creating sophisticated frequency tables with multiple class intervals

(9) Statistical Interpretation and Comparison: Drawing meaningful conclusions from complex statistical analyses

(10) Expert Problem-solving Techniques: Applying systematic approaches to solve challenging statistical problems with precision

Exceptional achievement! You have mastered expert-level statistical analysis and can handle complex real-world data problems with professional precision and analytical rigor!