Center and Spread Analysis
Grade 12 Math worksheet on calculating and interpreting measures of center (mean, median, mode) and spread (range, interquartile range, standard deviation) for various data sets.
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Center and Spread Analysis
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Read each question carefully and provide detailed answers. Show all your work for calculations.
1. The scores on a recent math test for two classes are given below:
Class A: 78, 85, 92, 70, 88, 75, 80, 95, 82, 79
Class B: 65, 90, 72, 88, 95, 78, 82, 60, 91, 84
a) Calculate the mean, median, and mode for Class A.
b) Calculate the mean, median, and mode for Class B.
c) Compare the measures of center for both classes. What do they tell you about the typical performance in each class?
2. Using the test scores from Question 1:
a) Calculate the range and interquartile range (IQR) for Class A.
b) Calculate the range and interquartile range (IQR) for Class B.
c) Compare the measures of spread for both classes. What do they tell you about the variability of scores in each class?
3. The standard deviation is a measure of . A small standard deviation indicates that data points are generally close to the , while a large standard deviation indicates that the data points are spread out over a wider range of values.
4. For the data set: 10, 12, 15, 18, 20, calculate the standard deviation. Show your steps.
5. Which of the following statements is true about a data distribution that is skewed to the right?
The mean is generally less than the median.
The mean and median are approximately equal.
The mean is generally greater than the median.
The mode is always the highest value.
6. True or False: The range is a more robust measure of spread than the interquartile range because it considers all data points.
True
False
7. A company recorded the number of sales made by its employees in a month. The data is as follows:
Sales: 15, 22, 18, 25, 12, 30, 20, 17, 28, 19, 32, 21, 24, 26, 16
a) Construct a box plot for this data set. (You may sketch the box plot on a separate sheet or describe its key features below.)
b) Identify any outliers using the 1.5 * IQR rule.
c) What does the shape of the distribution (from your box plot or by observing the data) suggest about the sales performance?