Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define modal class.
The modal class is the class interval with the
Perfect! Modal class contains the most frequently occurring values.
(2) What is the formula to find the mean using the assumed mean method?
Mean =
where
Excellent! This method simplifies calculations with large numbers.
(3) What is the class size of a class interval 35 – 45?
Class size =
Correct! Class size is always the difference between upper and lower limits.
(4) Write the relationship between mean, median and mode.
For a moderately skewed distribution: Mode =
Perfect! This is the empirical relationship for skewed distributions.
(5) If the mean of a distribution is 20, what is the sum of 25 observations?
Sum =
Excellent! Sum = Mean × Number = 20 × 25 = 500.
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) Find the mean of the following data:
| x | 5 | 10 | 15 | 20 |
|---|---|---|---|---|
| f | 2 | 4 | 6 | 8 |
Mean =
Mean =
Perfect! The mean is 15.
(2) Find the median of the following data:
| Marks | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| Students | 1 | 3 | 5 | 4 | 2 |
Position of median =
Total students = 1 + 3 + 5 + 4 + 2 =
Cumulative frequency: 1,
The 8th value lies in the group with marks
Excellent! The median is 30.
(3) Find the class mark of the class interval 75 – 85.
Class mark =
Perfect! Class mark is the midpoint of the interval since Class mark =
(4) Find the mode of the data: 3, 5, 7, 5, 3, 5, 8, 9, 3.
Mode =
Frequency count: 3 appears
Excellent! When two values have the same highest frequency, it's bimodal.
(5) Which measure of central tendency is least affected by extreme values?
The
Perfect! Median is the most robust measure against outliers.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Find the mean of the following data using the assumed mean method:
| Class Interval | Frequency |
|---|---|
| 10–20 | 5 |
| 20–30 | 8 |
| 30–40 | 10 |
| 40–50 | 6 |
| 50–60 | 1 |
Mean =
Excellent! The mean is approximately 31.67 as Mean = A +
(2) Find the median of the following distribution:
| Class Interval | Frequency |
|---|---|
| 0–10 | 2 |
| 10–20 | 4 |
| 20–30 | 7 |
| 30–40 | 6 |
| 40–50 | 1 |
Median =
The 10th value lies in class
Perfect! The median is approximately 25.71 given, Median = L +
(3) Find the mode of the following data:
| Class Interval | Frequency |
|---|---|
| 0–10 | 3 |
| 10–20 | 7 |
| 20–30 | 12 |
| 30–40 | 9 |
| 40–50 | 4 |
Mode =
Excellent! The mode is 26.25, given Mode = L +
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) Assumed mean method is used to simplify:
(a) Median calculation (b) Mode calculation (c) Mean calculation (d) Frequency counting
Correct! Assumed mean method simplifies mean calculation for large numbers.
(2) The midpoint of class 60–80 is:
(a) 70 (b) 65 (c) 60 (d) 75
Correct! Midpoint =
(3) The class interval with the highest frequency is called:
(a) Median class (b) Modal class (c) Central class (d) Frequency class
Correct! Modal class has the highest frequency.
(4) Which of these is not a measure of central tendency?
(a) Mean (b) Median (c) Frequency (d) Mode
Correct! Frequency is not a measure of central tendency.
(5) What is the sum of frequencies in a frequency distribution called?
(a) Class mark (b) Class width (c) Total observations (d) Median
Correct! Sum of frequencies gives total observations.
(6) Which central tendency is represented by the middle value of ordered data?
(a) Mode (b) Mean (c) Median (d) None
Correct! Median is the middle value when data is arranged in order.
(7) In a grouped frequency distribution, classes should be:
(a) Overlapping (b) Inclusive (c) Exclusive (d) Random
Correct! Classes should be mutually exclusive to avoid double counting.
(8) Mean is more affected by:
(a) Small numbers (b) Frequency (c) Extreme values (d) Class interval
Correct! Mean is sensitive to outliers and extreme values.
(9) The formula for mode using grouped data is:
(a) L +
Correct! This is the standard formula for mode in grouped data.
(10) The difference between upper and lower class boundaries is:
(a) Class mark (b) Class width (c) Frequency (d) Median
Correct! Class width is the difference between upper and lower boundaries.
Statistics Challenge
Determine whether these statements about statistics are True or False: