In a frequency table, f counts how many times a value x occurs. Thus x= fx f: weight each value by its frequency. For grouped intervals, use the midpoint as a representative value; the result is an estimate because the exact observations are lost. Example **Time t (min)** | **Frequency** | **Midpoint** 0<t 10 | 4 | 5 10<t 20 | 8 | 15 20<t 30 | 8 | 25 Estimated mean= 4(5)+8(15)+8(25)20=17 min. The boundary 10 belongs to the first interval here, not both. There are 12 observations at or below 20 minutes. The last two classes tie for highest frequency. A grouped table does not reveal the exact smallest or largest value. A modal class is a class with the greatest frequency. Two classes can tie. For a histogram, calculate frequency density separately so that bar area represents frequency, including when class widths differ.

In a frequency table, \(f\) counts how many times a value \(x\) occurs. Thus \(\overline{x}=\dfrac{\sum fx}{\sum f}\): weight each value by its frequency. For grouped intervals, use the midpoint as a representative value; the result is an estimate because the exact observations are lost.

\(\text{Estimated mean}=\dfrac{4(5)+8(15)+8(25)}{20}=17\text{ min}\).

The boundary \(10\) belongs to the first interval here, not both. There are \(12\) observations at or below \(20\) minutes. The last two classes tie for highest frequency. A grouped table does not reveal the exact smallest or largest value.

A modal class is a class with the greatest frequency. Two classes can tie. For a histogram, calculate frequency density separately so that bar area represents frequency, including when class widths differ.

Statistics

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Time \(t\) (min)	Frequency	Midpoint
\(0<t\le10\)	\(4\)	\(5\)
\(10<t\le20\)	\(8\)	\(15\)
\(20<t\le30\)	\(8\)	\(25\)

Frequency tables and grouped means

Frequency tables and grouped means