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Chapter 14: Statistics > Moderate Level Worksheet

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 = mean +

where di = xi - A (A = assumed mean)

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 = × Median - × Mean

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:

x5101520
f2468

Mean =

Mean = ΣfixiΣfi = 30020 = 15 with Σfi = 2 + 4 + 6 + 8 = and Σfixi = (5×2) + (10×4) + (15×6) + (20×8) = 10 + 40 + 90 + 160 =

Perfect! The mean is 15.

(2) Find the median of the following data:

Marks1020304050
Students13542

Position of median = th value

Total students = 1 + 3 + 5 + 4 + 2 = giving position of median = n+12 = 15+12 = 8th value

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 = Upper limit+Lower limit2

(4) Find the mode of the data: 3, 5, 7, 5, 3, 5, 8, 9, 3.

Mode =

Frequency count: 3 appears times, 5 appears times, others appear once. Since both 3 and 5 have the highest frequency, the data is

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 is least affected by extreme values because it depends only on 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 IntervalFrequency
10–205
20–308
30–4010
40–506
50–601

Mean =

Excellent! The mean is approximately 31.67 as Mean = A + ΣfidiΣfi .

(2) Find the median of the following distribution:

Class IntervalFrequency
0–102
10–204
20–307
30–406
40–501

Median = with Σfi = and position of median = th value

The 10th value lies in class (median class)

Perfect! The median is approximately 25.71 given, Median = L + n2CFf × h.

(3) Find the mode of the following data:

Class IntervalFrequency
0–103
10–207
20–3012
30–409
40–504

Mode = with Modal class =

Excellent! The mode is 26.25, given Mode = L + f1f02f1f0f2 × h

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

Median calculation
Mode calculation
Mean calculation
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

70
65
60
75

Correct! Midpoint = 60+802 = 70.

(3) The class interval with the highest frequency is called:

(a) Median class (b) Modal class (c) Central class (d) Frequency class

Median class
Modal class
Central class
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

Mean
Median
Frequency
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

Class mark
Class width
Total observations
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

Mode
Mean
Median
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

Overlapping
Inclusive
Exclusive
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

Small numbers
Frequency
Extreme values
Class interval

Correct! Mean is sensitive to outliers and extreme values.

(9) The formula for mode using grouped data is:

(a) L + f1f02f1f0f2 × h (b) L + f2f1f2+f1 × h (c) L+U2 (d) None of these

L + (f₁-f₀)/(2f₁-f₀-f₂) × h
L + (f₂-f₁)/(f₂+f₁) × h
(L+U)/2
None of these

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

Class mark
Class width
Frequency
Median

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

Most frequently occurring value
May not exist for some datasets
Middle value of ordered data
Sum of values divided by count
Arithmetic average
Value with highest frequency
50th percentile
Least affected by outliers
Mode
Median
Mean

Statistics Challenge

Determine whether these statements about statistics are True or False:

Median is less affected by extreme values than mean
Modal class always contains the mean
Mean can never be calculated for grouped data
All datasets must have a unique mode
Class mark is the midpoint of a class interval
Assumed mean method simplifies calculations

Statistics Quiz