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

Question 1

Calculate the interquartile range (IQR) of $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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Question 2

If a new data point $10$ is added to the set $S = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ , calculate the new mean.

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Question 3

Determine the median of the data set $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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Question 4

Compute the sum of all values in the data set $X = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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Question 5

How many values in $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ exceed the mean of the set?

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Question 6

The student is required to calculate the population variance of a given dataset using a specific formula, showing the steps for calculating the mean, sum of squares, and the final variance value.

Compute the population variance of the following dataset: $\{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ Use the formula $\sigma^2 = \frac{1}{N}\sum x_i^2 - \bar{x}^2$ .

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Question 7

Calculate the mean of the data set $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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Question 8

Determine the lower and upper quartiles ( $Q_1$ and $Q_3$ ) of the data set $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

[3]

Question 9

A dataset of 14 observations is given by $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

Calculate the population variance, $\sigma^2$ , for this dataset.

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Hence, find the population standard deviation, $\sigma$ , for this dataset.

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Question 10

Calculate the range of the data set $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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Question 11

Find the mode(s) of the data set $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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Question 12

Determine the number of data points in the set $x = \{2, 3, 6, 7, 4, 13, 19, 32, 14, 23, 7, 8, 12, 13\}$ .

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