Data and Statistics
A. The upper and lower values of the distribution describe the healthy range of physiological values.
B. The standard deviation characterises the dispersion of data, and the variance characterises the central tendency of the data.
C. The mean and range are statistics that are strictly only applicable to normally distributed data.
D. Sixty-eight percent of all data values will be within 1 SD from the mean.
Answer is D: Normally distributed data have this predictable relationship between their mean and the spread of values around the mean.
2. Median is a measure of central tendency. It may be defined as:
A. The value that has half the values greater than it and half less than it
B. The value that occurs most often
C. The distribution of values that has the mode, mean and average equal to each other
D. The sum of all values divided by the number of values.
Answer is A: Median is the mid-point of the number of measured values. The value that appears most often in a set of data is called the mode.
3. What is the standard deviation used for?
A. As a measure of central tendency
B. As a measure of dispersion
C. As a measure of the spread of data that are normally distributed
D. As a measure of the error of the mean value
Answer is C: B is also correct but is not as good an answer as choice C.
4. What information does the “standard deviation” of a mean value tell us? A. It gives us a healthy range of values for the measured physiological quantity.
B. It is the range within which 68% of measured values are found.
C. It tells us that the measured values are normally distributed.
D. It tells us the number of values that were used to calculate the mean.
Answer is B: C is also correct but choice B is the better answer.
5. What does the standard deviation of the mean represent? For values that are normally distributed, it represents:
A. The value above and below the mean that includes 68% of all data values
B. The difference between the highest data value and the lowest data value
C. The average of the difference between each data value and the mean value
D. The spread of the normal distribution
Answer is A: The term “standard” in the standard deviation of a distribution of measured values, means that it may be relied upon to encompass 68% of all measured values.
6. Which of the following statements applies to the statistic known as the “standard deviation”?
A. It is a measure of central tendency.
B. It is only applicable to qualitative measurements.
C. Standard deviation is also known as the “variance”.
D. 95% of all data lie within 2 SD of the mean.
Answer is D: This is the only true statement for normally distributed data. Standard deviation is the square root of the variance.
Note: The following three questions about the “central tendency” of data, rely on the following information. Consider the weekly earnings in dollars for ten workers to be: 400, 475, 475, 475, 500, 500, 525, 620, 630 and 660. These ten wages add to the total: $5260.
7. What is the “average” wage—technically referred to as the arithmetic mean?
A. $475
B. $500
C. $526
D. $5260
Answer is C: The arithmetic mean is the sum of the ten wages, divided by the number of wages (10). So $5260/10 = $526.
8. What is the “median” wage of these ten?
A. $475
B. $500
C. $526
D. $600
Answer is B: The median is the middle number. Half of the ten numbers are larger than (or equal to) the median and half are smaller. The wages have been arranged in ascending order: the fifth is $500 and the sixth is also $500. So half of the numbers are $500 or less and half are $500 or more. The median is midway between these two numbers and is $500.
9. What is the “mode” value of these ten wages?
A. $475
B. $500
C. $526
D. $620
Answer is A: Mode is the most commonly occurring value. $475 appears three times so is the mode.
10. The mean June midday temperature in Desertville is 36 °C and the standard deviation (SD) is 3 °C. Assuming the temperature data for June to be normally distributed, how many days (to the nearest whole day) in June would you expect the midday temperature to be between 39 and 42 °C? (Hint: how many SDs are these two temperatures from the mean?)
A. 3
B. 14
C. 7
D. 4
Answer is D: 39 °C is 1 SD above the mean and 42 °C is 2 SD above the mean. Sixty-eight percent of values lie within 1 SD of the mean and 95% lie within 2 SD of the mean. Therefore, 27% of days (95 − 68 = 27%) would have a temperature between 30 and 33 °C or 39 and 42 °C. Hence we would expect the temperature to be between 39 and 42 °C on half of 27% (i.e. 13.5%) of the days in June. There are 30 days in June. So 13.5% of 30 = 0.135 × 30 = 4.05 = 4 to the nearest day.
11. For the distribution of data that is “normally distributed” what can be said of the mean, median and mode?
A. They have the same value.
B. The mean is lower than the median and mode.
C. The mean is higher than the median and the mode.
D. They cannot take on the same value.
Answer is A: In a perfectly normal distribution, the mean, median and mode have the same value.
12. The healthy male range for the physiological variable blood haemoglobin concentration is about 130–160 g/L. How is this range determined?
A. It is ±1 SD from the mean value.
B. It is ±2 SD from the mean value.
C. It is ±3 SD from the mean value.
D. It is the minimum and maximum value found for healthy males.
Answer is B: The reference interval comprises a range of ±2 SD from the mean. It indicates the limits that should cover 95% of normal subjects. That is 5% of healthy individuals will fall outside this range.
13. Many measured human physiological variables are found to have a normal distribution. For example, the mean fasting blood glucose is 4.7 mmol/L with a range: of 3.8–5.5 mmol/L. What does the healthy range signify?
A. Most healthy individuals will have blood glucose within this range.
B. All healthy individuals will have blood glucose within this range.
C. Individuals whose blood glucose is outside this range are unhealthy.
D. Five percent of healthy individuals will have blood glucose outside this range.
Answer is D: With “normally distributed” data there is a quantitative relationship between the mean value and the spread of values about the mean. The “healthy range” is taken to be ±2 SD from the mean value. It is well known that 95% of values will fall into this range. And also that 5% of healthy folk will have a value outside of this range.