State which of the following represent discrete data and which represent continuous data:(a) Numbers of shares sold each day in the stock market
(b) Temperatures recorded every half hour at a weather bureau
(c) Lifetimes of television tubes produced by a company
(d) Yearly incomes of college professors
(e) Lengths of 1000 bolts produced in a factory
The Correct Answer and Explanation is :
To determine which data is discrete and which is continuous, let’s first understand the difference between the two:
- Discrete data consists of distinct, separate values or counts. It is typically finite and often involves whole numbers (e.g., counts of items, number of occurrences).
- Continuous data can take any value within a given range. It is often measured and can be infinitely subdivided, usually involving real numbers (e.g., measurements like height, weight, temperature).
Now, let’s classify each item:
(a) Numbers of shares sold each day in the stock market:
This is discrete data because the number of shares sold is counted in whole numbers. There can’t be a fractional share (e.g., you can’t sell 2.5 shares; it’s either 2 or 3). Hence, the values are distinct, and each number is a count.
(b) Temperatures recorded every half hour at a weather bureau:
This is continuous data. Temperature can take any value within a range and can be measured with infinite precision (e.g., 22.3°C, 22.33°C, 22.333°C, etc.). Even though the data is recorded at specific intervals (every half hour), temperature itself is a continuous variable.
(c) Lifetimes of television tubes produced by a company:
This is continuous data. Lifetimes are typically measured (e.g., in hours, years, or cycles) and can take any value within a range. Although we might round these values when reporting, in theory, the lifetime could be any non-negative number and can be infinitely divided.
(d) Yearly incomes of college professors:
This is continuous data, even though income is often reported in whole numbers. Income can vary with infinite precision and is not restricted to integer values. For instance, a professor might earn $50,000.50, or $50,000.75, reflecting its continuous nature.
(e) Lengths of 1000 bolts produced in a factory:
This is continuous data. Lengths can be measured with precision, and they can take any real value within a specified range. A bolt may be 10.24 cm, 10.245 cm, or 10.246 cm, illustrating that the measurement can be infinitely subdivided.
Explanation Summary:
- Discrete data: Counts of items, events, or occurrences, like the number of shares or bolts.
- Continuous data: Measurements that can take any value within a range and are usually represented with real numbers, like temperature, lifetime, and income.