RV-18-001 · Histogram: recover the total and estimate a percentile

The histogram summarises task durations. The frequency densities are 5, 6 and 2 for 0–10, 10–30 and 30–60 minutes respectively.

(a) Work out the total number of tasks.

(b) Estimate the 75th percentile of the duration. State your assumption.

Part (a) Histograms ("cow food") & Linear Interpolation of Percentiles Booklet p. 67 & p. 72

Method

1) Use f = c.w × f.d for each bar and sum for total N

2) Locate 0.75N in cumulative frequency and use LB + (distance into group / freq of group) × c.w

Worked Example (RV-18-001 · Part (a))

Work out the total number of tasks.

Booklet p. 72:

\text{Frequency Density (f.d)} = \frac{\text{Frequency (f)}}{\text{Class Width (c.w)}}

1) Frequency = class width × frequency density.

2) Frequencies 50, 120, 60.

3) 230

230

Part (b) Histograms ("cow food") & Linear Interpolation of Percentiles Booklet p. 67 & p. 72

Method

1) Use f = c.w × f.d for each bar and sum for total N

2) Locate 0.75N in cumulative frequency and use LB + (distance into group / freq of group) × c.w

Worked Example (RV-18-001 · Part (b))

Estimate the 75th percentile of the duration. State your assumption.

Booklet p. 72:

\text{Frequency Density (f.d)} = \frac{\text{Frequency (f)}}{\text{Class Width (c.w)}}

1) Locate cumulative frequency 172.5.

2) 31.25 minutes

3) Assume a uniform distribution within the relevant class.

31.25 minutes; assume durations are uniformly distributed within each class.