Arithmetic Mean of Grouped Data

To determine the arithmetic mean of grouped data, use the following formula, where f is the frequency and M is the class midpoint: `x̄ = Σ(fM)/n`.

Using the group data below, the arithmetic mean is `() x̄ Σ(fM)/n = (572)/(24) ≈ 23.8` (seconds).

Time (in seconds) Frequency `f` Class Midpoint `M` `fM`
15–18.99 7 `(15 + 19)/2 = 17` `7 * 17 = 119`
19–22.99 6 `(19 + 23)/2 = 21` `6 * 21 = 126`
23–26.99 3 `(23 + 27)/2 = 25` `3 * 25 = 75`
27–30.99 3 `(27 + 31)/2 = 29` `3 * 29 = 87`
31–34.99 5 `(31 + 35)/2 = 33` `5 * 33 = 165`
Total `Σf = 24` `ΣfM = 572`