Questions: Fill in the blank. Shifting data, by adding a constant to each data value, does not change the median standard deviation. quartiles. mean

Fill in the blank. Shifting data, by adding a constant to each data value, does not change the median standard deviation. quartiles. mean
Transcript text: Fill in the blank. Shifting data, by adding a constant to each data value, does not change the $\square$ median standard deviation. quartiles. mean
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Solution

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Solution Steps

To determine which statistical measures remain unchanged when a constant is added to each data value, we need to consider how each measure is calculated. The median and quartiles are measures of position and are not affected by shifting the data. The standard deviation, which measures spread, also remains unchanged. However, the mean, which is a measure of central tendency, will change by the amount of the constant added.

Step 1: Understanding the Effect of Shifting Data

When a constant is added to each data value in a dataset, the entire dataset is shifted by that constant. This affects measures of central tendency but not measures of spread or position.

Step 2: Analyzing Measures of Central Tendency

The mean of a dataset is calculated as the sum of all data values divided by the number of values. If a constant \( c \) is added to each data value, the new mean becomes the original mean plus \( c \). Therefore, the mean changes when data is shifted.

Step 3: Analyzing Measures of Spread

The standard deviation is a measure of how spread out the numbers in a dataset are. It is calculated based on the differences between each data value and the mean. Adding a constant \( c \) to each data value does not affect these differences, so the standard deviation remains unchanged.

Step 4: Analyzing Measures of Position

The median and quartiles are measures of position within a dataset. They depend on the order of the data values rather than their specific values. Shifting all data values by a constant does not change their order, so the median and quartiles remain unchanged.

Final Answer

Shifting data by adding a constant does not change the median, standard deviation, or quartiles. Therefore, the answer is: \[ \boxed{\text{median, standard deviation, quartiles}} \]

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