Exercises for Question Type 7: Determining the effect on mean, mode, median, range, variance, standard deviation and IQR given specific transformations of data

Question 1

If the smallest value of a dataset is decreased by 3 (others unchanged), describe the effect on mean, median, mode, range, variance, standard deviation, and IQR.

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Question 2

A dataset has a minimum value m and a maximum value M . The maximum value is increased to M + 1 and the minimum value is decreased to m - 1 . State how the mean, median, mode, range, variance, standard deviation, and interquartile range (IQR) change.

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Question 3

Transform each value by x_{i}^{'} = 5 x_{i} + 10 . Describe the effect on the mean, median, mode, range, variance, standard deviation and IQR.

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Question 4

A dataset has minimum m and maximum M . You replace M by 2 M and m by m /2, leaving other values unchanged. Describe the changes to mean, median, mode, range, variance, standard deviation, and IQR.

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Question 5

Consider a dataset x_{1}, \dots, x_{n} . Each value is multiplied by 3 to form a new dataset where x_{i}^{'} = 3 x_{i} . State how the mean, median, mode, range, variance, standard deviation, and interquartile range (IQR) change.

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Question 6

Suppose you multiply every data value by - 2 . How do mean, median, mode, range, variance, standard deviation, and IQR change?

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Question 7

If you add 7 to the maximum value and subtract 7 from the minimum value of a dataset (others unchanged), how are mean, median, mode, range, variance, standard deviation, and IQR affected?

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Question 8

If every data point is divided by 4, state the changes to mean, median, mode, range, variance, standard deviation, and IQR.

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Question 9

Transform a dataset to z-scores via z_{i} = \frac{x _{i} - x ˉ}{s}, where s is the original standard deviation. Explain the effect on mean, median, mode, range, variance, standard deviation, and IQR.

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Question 10

Consider a dataset of n values where n is large and the mode is not the largest value. The largest value of the dataset is increased by 5, while all other values remain unchanged.

(a)

State the effect on the mean, median, and mode.

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(b)

State the effect on the range, variance, standard deviation, and interquartile range (IQR).

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Question 11

Suppose a dataset consists of values x_{1}, x_{2}, \dots, x_{n} . If every value is increased by 4 to form a new dataset x_{i}^{'} = x_{i} + 4, determine how the following summary statistics change: mean, median, mode, range, variance, standard deviation, and IQR.

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Question 12

A dataset x_{1}, \dots, x_{n} has mean \overset{x}{ˉ} .

The dataset is transformed by y_{i} = x_{i} - \overset{x}{ˉ} (mean-centering). Determine the new mean, median, mode, range, variance, standard deviation, and interquartile range (IQR) in terms of the original statistics.

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IB Mathematics Analysis and Approaches Question Type 7: Determining the Effect on Mean, Mode, Median, Range, Variance, Standard Deviation and IQR Given Specific Transformations of Data Exercises