1. Find the following quantities by hand (except for the standard deviation) Check your results with your calculator:
a. Minimum
b. Lower Quartile
c. Median
d. Upper Quartile
e. Maximum
f. Range
g. Mean
h. Mode
i. Standard deviation
2. Is the mean or median a better measure of central tendency in this case? Justify your answer.
3. What does the standard deviation tell you about the spread of this data? Explain.
1. To find the following quantities by hand (except for the standard deviation), follow these steps:
a. Minimum: Find the smallest value in the dataset.
b. Lower Quartile: Arrange the data in ascending order. Locate the 25th percentile by multiplying the total number of data points by 0.25. If the result is not an integer, round it up to the nearest whole number. The lower quartile is the value at this position.
c. Median: Arrange the data in ascending order. If the total number of data points is odd, the median is the middle value. If the total number of data points is even, the median is the average of the two middle values.
d. Upper Quartile: Arrange the data in ascending order. Locate the 75th percentile by multiplying the total number of data points by 0.75. If the result is not an integer, round it up to the nearest whole number. The upper quartile is the value at this position.
e. Maximum: Find the largest value in the dataset.
f. Range: Subtract the minimum value from the maximum value.
g. Mean: Calculate the sum of all the values in the dataset and divide it by the total number of data points.
h. Mode: Find the value(s) that occur most frequently in the dataset. It can be zero, one, or multiple modes.
i. Standard deviation: Use a calculator or statistical software to calculate the standard deviation. This calculation involves several steps and formulas, making it more complex to do by hand.
2. To determine whether the mean or median is a better measure of central tendency, consider the nature of the data. If the data is skewed or contains outliers, the median is usually a better measure. The median is less affected by extreme values. If the data is normally distributed without outliers, the mean provides a better representation as it takes into account all values. Justify your answer by analyzing the data distribution and considering the characteristics of the mean and median.
3. The standard deviation tells you about the spread or dispersion of the data. It measures how much the values vary from the mean. A larger standard deviation indicates greater variability in the data, while a smaller standard deviation indicates less variability. In other words, the standard deviation provides a measure of how spread out the data is around the mean. This information is useful for understanding the consistency or variability of the dataset and comparing different datasets.