Hard Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) What is the formula to calculate the mode in grouped data? Mode = + f1−f02f1−f0−f22f1−f0−f2f1−f0f0−f12f2−f0−f1 × , where l = lower of modal class, f1 = of class, f0 = of class, f2 = of class, h = class

Perfect! This is the standard formula for mode in grouped data.

(2) Define cumulative frequency. Cumulative frequency is the of frequencies up to a particular class, showing the total number of observations below or up to that .

Excellent! Cumulative frequency helps in finding median and percentiles.

(3) What is the median class? The median class is the class that contains the value, identified as the class where the cumulative frequency is equal to or just exceeds .

Perfect! This is how we locate the median in grouped data.

(4) What do we call the average of the lower and upper boundaries of a class? Class markClass midpoint or class midpoint

Correct! Class mark = Lower boundary + Upper boundary2.

(5) State one advantage of using the assumed mean method over the direct method. It reduces computational complexity when dealing with numbers or makes calculations easiercomplex.

Excellent! Assumed mean method simplifies calculations significantly.

Short Answer Questions (2 Marks Each)

(1) The mean of 10 numbers is 25. If one number is removed and the new mean becomes 24, find the number that was removed. Number removed =

Perfect! Used the relationship between mean and sum effectively.

(2) Find the class width and class mark for the interval 45–60.

Class width =

Class mark =

Excellent! Both calculations are correct.

(3) Which is more suitable to measure central tendency: mean, median, or mode? Justify with an example.

depends on the data type and distributionMean reliable the most out of allMean and Median both.

for symmetric data with for skewed data with outliers and for categorical data.

Perfect understanding of when to use each measure!

(4) A class has 30 students. The marks out of 20 are grouped as follows: Marks (out of 20): 0–5 (4 students), 5–10 (8 students), 10–15 (10 students), 15–20 (8 students). Identify the modal class.

Modal class =

Perfect! Correctly identified the class with maximum frequency.

(5) A grouped frequency distribution has the modal class 30–40 with f1 = 15, f0 = 10, and f2 = 12. Class width is 10. Find the mode.

Mode =

Excellent application of the mode formula!

Long Answer Questions (4 Marks Each)

(1) Find the mean using assumed mean method: Class intervals: 0–10 (3), 10–20 (7), 20–30 (12), 30–40 (17), 40–50 (7), 50–60 (4). Mean =

Excellent systematic application of assumed mean method!

(2) Calculate the median of the following data: Class intervals: 10–20 (6), 20–30 (8), 30–40 (10), 40–50 (12), 50–60 (4). Median =

Perfect application of median formula for grouped data!

(3) Calculate the mode from the given data: Class intervals: 0–10 (5), 10–20 (8), 20–30 (15), 30–40 (10), 40–50 (7). Mode = (upto two decimal places)

Excellent! Mode ≈ 25.83 using the standard formula.

Part B: Objective Questions (1 Mark Each)

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

(1) Which of the following is used for finding central tendency in a large grouped dataset?

(a) Pie Chart (b) Histogram (c) Bar Graph (d) Frequency Polygon

Correct! Histograms visually show the modal class and help identify central tendency.

(2) Median is useful when:

(a) All data is equal (b) Data has outliers (c) Data is uniform (d) None of these

Correct! Median is not affected by extreme values (outliers).

(3) Mode is the value:

(a) That appears once (b) That appears most often (c) That is the largest (d) That is the smallest

Correct! Mode is the value with the highest frequency.

(4) If the frequencies of the modal class and two adjacent classes are equal, then:

(a) Mode doesn't exist (b) Median is used (c) More data is needed (d) Mode = Median

Correct! When frequencies are equal, we need more data to determine the true modal class.

(5) Median class is the class:

(a) With max frequency (b) With mid cumulative frequency (c) With least width (d) With smallest value

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

(6) If a data set has multiple modes, it is called:

(a) Monomodal (b) Bimodal (c) Multimodal (d) Unimodal

Correct! Multimodal means having more than two modes.

(7) In grouped data, mode is located using:

(a) Graph (b) Formula (c) Histogram (d) Both B and C

Correct! Mode can be found using formula or by observing the highest bar in histogram.

(8) Which measure of central tendency always lies between the highest and lowest values?

(a) Mean (b) Median (c) Mode (d) All of these

Correct! All measures of central tendency lie within the range of data values.

(9) Mean is not a good measure of central tendency when:

(a) All values are positive (b) Data is uniform (c) There are outliers (d) There are few entries

Correct! Outliers significantly affect the mean, making it less representative.

(10) Mode of grouped data is found by:

(a) Adding all midpoints (b) Highest frequency class (c) Smallest class width (d) Largest lower limit

Correct! Mode is located in the class with the highest frequency (modal class).

Statistics Challenge

Determine whether these statements about statistics are True or False:

Statistics Quiz

🎉 You Did It! What You've Learned:

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

(1) Measures of Central Tendency: Mean, median, and mode for grouped data

(2) Calculation Methods: Direct method and assumed mean method for finding mean

(3) Median in Grouped Data: Using cumulative frequency and median formula

(4) Mode in Grouped Data: Identifying modal class and applying mode formula

(5) When to Use Each Measure: Choosing appropriate measure based on data characteristics

(6) Class Concepts: Class mark, class width, and cumulative frequency

(7) Formula Applications: Systematic use of statistical formulas for grouped data

(8) Real-world Applications: Analyzing practical datasets and drawing conclusions

Excellent work mastering advanced statistical concepts and their practical applications!