Descriptive Statistics

This resource is designed to help students understand:

• Different averages: the mean and the median.

• Measures of spread: the standard deviation and the interquartile range.

• Statistical diagrams: histograms and boxplots.

Self teaching notes and questions are contained on the work cards.

Mean and Standard Deviation: Students are given five numbers. The mean, variance and standard deviation have been calculated, showing each step of the calculations. Work card 1.1 leads students through exercises which explore the effect on the mean and standard deviation of changing the original five numbers.

Mean and Median: A frequency distribution of students' examination marks is given for which the mean and median have been calculated and displayed on a histogram. Work card 1.2 asks students to explore the effect on the value of the mean, the median and the shape of the distribution as the frequencies are changed.

Standard Deviation and inter Quartile range: A frequency distribution of students' examination marks is given for which the standard deviation and interquartile range have been calculated and displayed on a histogram. Work card 1.3 asks students to explore the effect on the value of the standard deviation and the interquartile range as the frequencies are changed.

Boxplots: A data set of 48 numbers is given. The median, quartiles, interquartile range and fences have been calculated and the boxplot and outliers plotted. Work card 1.4 explores the effect on the boxplots of altering the original data.

Histograms: A data set of 48 numbers is given which is tallied into seven classes of unequal width. The resulting histogram is displayed. Work card 1.5 explores how the histogram changes as the data values and class intervals are altered.

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This resource is part of Discovering Important Statistical Concepts using Spreadsheets (DISCUS)

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