CA Foundation · Quantitative Aptitude · Statistical Description of Data
A retail chain collected the heights (in cm) of 50 shelf units. The first quartile (Q1) is 145 cm and the third quartile (Q3) is 165 cm. What is the interquartile range (IQR) of the shelf heights?
The interquartile range is the difference between the third and first quartiles. IQR = 165 - 145 = 20 cm. This measures the spread of the central 50% of observations and is particularly useful for identifying outliers and comparing variability across datasets.
- A10 cm
- B20 cmCorrect
- C30 cm
- D155 cm
Explanation
The interquartile range is defined as IQR = Q3 - Q1. Given Q3 = 165 cm and Q1 = 145 cm, IQR = 165 - 145 = 20 cm. The IQR represents the range of the middle 50% of the data and is a robust measure of spread that is unaffected by extreme values. Option 3 (30 cm) would result from incorrect arithmetic; option 4 confuses IQR with the median.
Did you get it right without looking?
One question tells you little. A timed set on Statistical Description of Data shows your real accuracy, how long you take and where you lose marks.
More Statistical Description of Data questions
- In the layout of a statistical table, the descriptive headings given to the rows are collectively known as:
- A frequency distribution of daily wages (in ₹) of workers in a factory is given as: Wages (₹): 200–300, 300–400, 400–500, 500–600 Frequency…
- For a firm's 50 employees, the 'more than' cumulative frequencies of age (in years) are: more than 10: 50; more than 20: 42; more than 30: 3…
- A statistician in Chennai has 64 observations and wants to decide the number of classes using Sturges' rule, k = 1 + 3.322 log₁₀ N. Given lo…
- The monthly budget of Mr. Iyer's household is ₹1,80,000, of which ₹54,000 is spent on education. In a pie chart of the budget, the angle at …
- A frequency table uses inclusive class intervals 10–19, 20–29, 30–39 and so on. What are the true class boundaries of the class 20–29?