Organisation of Data (Classification, Series, Frequency Distribution) — Practice

Question 1

Name the four types of data classification and give one example of each.

Accepted Answer

1. Geographical classification: Data classified by location/region. Example: State-wise GDP of India. 2. Chronological classification: Data classified by time periods. Example: Year-wise inflation rate from 2010 to 2024. 3. Qualitative classification: Data classified by non-numerical attribute. Example: Workers classified by occupation (farming, manufacturing, services). 4. Quantitative classification: Data classified by numerical measurement into groups. Example: Students classified by marks into 0–20, 21–40, 41–60, 61–80, 81–100.

Question 2

Construct a frequency distribution table using exclusive class intervals of width 10 for the following marks of 20 students: 15, 28, 35, 42, 56, 68, 72, 85, 19, 33, 47, 61, 74, 88, 26, 51, 64, 79, 92, 38

Accepted Answer

Step 1: Find range = 92 − 15 = 77. Step 2: Class width = 10. Start from 10. Classes: 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90, 90–100. Step 3: Sort values into classes using tally marks. 10–20: 15, 19 → frequency = 2. 20–30: 28, 26 → frequency = 2. 30–40: 35, 33, 38 → frequency = 3. 40–50: 42, 47 → frequency = 2. 50–60: 56, 51 → frequency = 2. 60–70: 68, 61, 64 → frequency = 3. 70–80: 72, 74, 79 → frequency = 3. 80–90: 85, 88 → frequency = 2. 90–100: 92 → frequency = 1. Total frequency = 20. Step 4: Add cumulative frequency column: 2, 4, 7, 9, 11, 14, 17, 19, 20.

Question 3

The following data represents monthly income (₹000) of 25 workers: 12, 18, 25, 31, 45, 52, 8, 22, 37, 48, 15, 29, 42, 55, 9, 20, 34, 46, 58, 11, 27, 39, 51, 17, 44. (a) Construct a frequency distribution using exclusive class intervals of width 10 starting from 0. (b) Calculate the mid-point of each class. (c) State the difference between inclusive and exclusive class intervals.

Accepted Answer

Step 1: Range = 58 − 8 = 50. Width = 10. Classes: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60. Step 2: Frequency distribution: 0–10: 8, 9 → f = 2; Mid-point = 5. 10–20: 12, 18, 15, 11, 17 → f = 5; Mid-point = 15. 20–30: 25, 22, 29, 20, 27 → f = 5; Mid-point = 25. 30–40: 31, 37, 34, 39 → f = 4; Mid-point = 35. 40–50: 45, 48, 42, 46, 44 → f = 5; Mid-point = 45. 50–60: 52, 55, 51, 58 → f = 4; Mid-point = 55. Total = 25. ✓ (c) Difference between inclusive and exclusive: Exclusive class intervals (10–20, 20–30): The upper limit is EXCLUDED from that class. A value of exactly 20 belongs to the NEXT class (20–30), not the first (10–20). Used for continuous variables. Inclusive class intervals (10–19, 20–29): The upper limit is INCLUDED in that class. A value of 19 belongs to the first class (10–19). Used for discrete variables or when presenting data with whole numbers. To convert inclusive to exclusive, subtract 0.5 from each lower limit and add 0.5 to each upper limit.

Practice — Organisation of Data (Classification, Series, Frequency Distribution)

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