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Question

Difficulty: HardMeasures of Central Tendency

A medical detachment is tracking a patient's resting heart rate over a six-day period. The mean heart rate over the six days is 6969 beats per minute (bpm). The readings for five of those days are 6666, 7272, 6868, 7878, and 6565. What is the median heart rate for the entire six-day period?

Answer: 67 bpm

Answer

67
The correct answer is derived in two phases. First, the missing sixth value is found by subtracting the sum of the five known values (349) from the total sum of all six values (69 * 6 = 414), which yields 65. Second, all six values are sorted from least to greatest: 65, 65, 66, 68, 72, 78. Since there are 6 values, the median is the exact average of the two middle numbers (66 and 68). (66 + 68) / 2 = 67 bpm.

Step-by-Step Solution

1
Calculate the total sum of the heart rates for all six days.
414414
The total sum is required to find the value of the missing sixth day. Multiply the given mean (6969) by the total number of days (66).
2
Calculate the sum of the five known heart rates.
349349
Adding the given values (66+72+68+78+6566 + 72 + 68 + 78 + 65) allows us to see how much of the total sum is accounted for.
3
Determine the heart rate for the sixth day.
6565
Subtracting the sum of the known days (349349) from the total sum (414414) reveals the missing data point.
4
Arrange all six heart rates in ascending order.
65,65,66,68,72,7865, 65, 66, 68, 72, 78
The median is a measure of position, which strictly requires the entire dataset to be ordered from least to greatest.
5
Identify the two middle values and calculate their average.
6767
Because there is an even number of values (n=6n=6), the median is the mean of the 3rd and 4th values: (66+68)/2(66 + 68) / 2.

Key Concept

Solving for a missing data value using the arithmetic mean, followed by determining the median of an even-numbered dataset.
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Topics

Measures of Central Tendency

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