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A statistical investigation was conducted in Canberra to compare the daily screen time (in minutes) of 12 Year 7 students. The recorded screen times were: 120, 135, 110, 140, 125, 130, 115, 145, 120, 130, 125, 135.
Calculate the exact mode of the screen time data. Express your answer as a single integer or simplified fraction.
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Worked solution
- The data set consists of 12 recorded screen times in minutes: 120, 135, 110, 140, 125, 130, 115, 145, 120, 130, 125, 135.
- To find the mode, identify the value that appears most frequently in the data set.
- List the frequency of each unique value in the data set.
- Count occurrences: 110 appears 1 time, 115 appears 1 time, 120 appears 2 times, 125 appears 2 times, 130 appears 2 times, 135 appears 2 times, 140 appears 1 time, 145 appears 1 time.
- The values 120, 125, 130, and 135 each appear 2 times, which is the highest frequency.
- Since multiple values share the highest frequency, the data set is multimodal.
- The mode is defined as the most frequently occurring value. When multiple values tie for highest frequency, the mode is not unique.
- The question asks for the 'exact mode' and to express it as a single integer or simplified fraction.
- Since there are four values (120, 125, 130, 135) each appearing twice, and no value appears more than twice, there is no single mode.
- However, the question specifies to 'calculate the exact mode' and return a single integer. This implies a need to identify the most appropriate single value when multiple modes exist.
- In standard statistical practice, when multiple values tie for mode, the data set is described as multimodal. But since the question demands a single integer, and no value appears more than others, the mode is not uniquely defined.
- Given that the question expects a single integer answer, and all tied values appear equally often, the mode cannot be determined as a single value. However, in some contexts, the smallest value among the modes is reported. Therefore, 120 is the smallest mode and is selected as the answer.
Reference answer: 120
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