Vanessa has 17 quarters, 8 dimes, 15 pennies, and 14 nickels in a piggy bank. Which of the following measures of central tendency will change if she spends 4 quarters to get a soft drink?
Mean, median, mod, or none will change?
Why?
I think the mode is going to change
Mode will change
The measure of central tendency that will change if Vanessa spends 4 quarters to get a soft drink is the mean.
The mean is calculated by finding the average of a set of numbers. In this case, the set of numbers represents the number of each type of coin in Vanessa's piggy bank.
If Vanessa spends 4 quarters, the number of quarters in her piggy bank will decrease from 17 to 13. This change in the data set will affect the mean because the total sum of all the coins will be reduced. Consequently, the average value of the coins will be lower, resulting in a different mean.
On the other hand, the median, mod, and mode will not be affected by spending 4 quarters because these measures are not influenced by changes in individual values or outliers.
To determine which measure of central tendency will change if Vanessa spends 4 quarters, we need to understand what each measure represents and how it is affected by the data.
1. Mean: The mean is obtained by adding up all the values in a data set and then dividing by the total number of values. In this case, the mean can be calculated by adding the values of all the different coins (quarters, dimes, pennies, and nickels), dividing by the total number of coins (54), and finding the average value.
2. Median: The median is the middle value in a data set when arranged in ascending or descending order. To find the median, we would arrange the different coins in numerical order and then identify the coin in the middle.
3. Mode: The mode is the value that occurs most frequently in a data set. In this case, we would determine which type of coin (quarters, dimes, pennies, or nickels) appears most often.
Now, let's analyze how spending 4 quarters will affect these measures:
- Mean: If Vanessa spends 4 quarters, the total number of coins will decrease from 54 to 50, but the total value of coins will also decrease. Thus, the mean value will change.
- Median: Spending 4 quarters will not affect the arrangement of the coins, so the median value will remain the same.
- Mode: The most frequently occurring coin type will not change, so the mode will remain the same.
Therefore, the measure of central tendency that will change if Vanessa spends 4 quarters is the mean.