The table below shows the speed distribution (in km/h) recorded for 50 vehicles passing a police checkpoint on a highway: | Speed Interval (km/h) | Frequency (f) | | :---: | :---: | | 40 - 49 | 6 | | 50 - 59 | 12 | | 60 - 69 | 18 | | 70 - 79 | 10 | | 80 - 89 | 4 | Calculate the mean speed of the veh

The table below shows the speed distribution (in km/h) recorded for 50 vehicles passing a … — JAMB UTME

The table below shows the speed distribution (in km/h) recorded for $50$ vehicles passing a police checkpoint on a highway:

Calculate the mean speed of the vehicles.

Answer: 63.3 km/h

The mean speed of the vehicles is

63.3\text{ km/h}

The mean of a grouped frequency distribution is computed using the formula

\bar{x} = \frac{\sum fx}{\sum f}

. The midpoints (

x

) for the intervals are

44.5, 54.5, 64.5, 74.5,

and

84.5

. Multiplying these midpoints by their respective frequencies yields products totaling

3165

. Dividing this total by the total number of vehicles (

50

) gives a mean speed of

63.3\text{ km/h}

Find the class midpoints (

x

) for each speed interval

Midpoints are

x_1 = 44.5

x_2 = 54.5

x_3 = 64.5

x_4 = 74.5

, and

x_5 = 84.5

The midpoint of a grouped class interval is calculated as

\frac{\text{Lower limit} + \text{Upper limit}}{2}

Calculate the product

fx

for each class

6 \times 44.5 = 267

12 \times 54.5 = 654

18 \times 64.5 = 1161

10 \times 74.5 = 745

, and

4 \times 84.5 = 338

Multiplying class midpoint by frequency estimates the total contribution of all items within that interval.

Find total frequency

\sum f

and sum of products

\sum fx

\sum f = 6 + 12 + 18 + 10 + 4 = 50

and

\sum fx = 267 + 654 + 1161 + 745 + 338 = 3165

Summing frequencies gives total sample size, and summing

fx

gives estimated grand total.

Compute the estimated mean speed

\bar{x} = \frac{\sum fx}{\sum f} = \frac{3165}{50} = 63.3\text{ km/h}

The standard formula for the mean of grouped frequency data is

\bar{x} = \frac{\sum fx}{\sum f}

Grouped Mean Calculation