Weekly Instruction Time The Organization for Economic Cooperation and Development provided the following mean weekly instruction times (hours) for elementary and high school students in various countries: 22.2 (United States); 24.8 (France); 24.2 (Mexico); 26.9 (China); 23.8 (Japan). Use the five given times for the following.
a. Find the mean.
b. Find the median.
c. Find the range.
d. Find the standard deviation.
e. Find the variance.
f. Use the range rule of thumb to identify the range of usual values.
g. Based on the result from part (f), are any of the times unusual? Why or why not?
h. What is the level of measurement of the data: nominal, ordinal, interval, or ratio?
i. Are the data discrete or continuous?
j. There is something fundamentally wrong with using the given times to find statistics such as the mean. What is wrong?
Given that, the Organization for Economic Cooperation and Development provided the following mean weekly instruction times (hours) for elementary and high school students in various countries: 22.2 (United States); 24.8 (France); 24.2 (Mexico); 26.9 (China); 23.8 (Japan).
Given the mean weekly instruction times for elementary and high school students in various countries.
a). The mean is given by
= 24.38 hours.
Therefore mean = 24.4 hours.
b). Here we have to arrange the data in ascending or descending order.
The median is the third observation in the arranged data.
Thus the median is 24.2.
c). The range is given by
Range (R) =
= 26.9 - 22.2 = 4.7.
Therefore the range is 4.7.
d). The standard deviation is given by
Therefore the standard deviation is 1.71.
e). Variance is given by
f). Using the range rule of thumb,
Minimum = μ – 2σ
= 24.4 - 2(1.71)
Maximum = μ + 2σ
=24.4 + 2(1.71)
g). Not one of the times is unusual since all observations are within the usual range of values.
h). The level of measurement is ratio since both the difference and ratio of each data are meaningful.
i). The data is continuous since it can assume any positive real number.
j). The given times come from countries with very different population sizes, so it does not make sense to treat the given times equally. Calculations of statistics should take the different population sizes into account. Also, the sample is very small, and there is no indication that the sample is random.