over a period of many months, a particular 5 year old boy's play activity was observed. the length of time spent in each episode of play with toys was recorded. the paper "a temporal analysis of free toy play and distractibility in young children" (journal of experimental child psychology, 1991,pages 41-69) reported the accompanying data on the play-episode lengths. use the data to calculate the density for the 20 to < 40 minute period.

The density value for the 20 to < 40 minute period is the ratio of the frequency to the total frequency of the distribution, which is 0.146

The Density for the 20 to < 40 minute period is given by the relative frequency value of the given length of time :

Relative frequency = Frequency / Cummulative frequency

Cummulative frequency = (54 + 44 + 28 + 21 + 31 + 15 + 6 + 5 + 8) = 212

Frequency of the 20 to < 40 period = 31

The Density value for the period is :

31 / 212 = 0.146

Therefore, the density value for the 20 to less than 40 period is 0.146.

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