Mean, Median, Mode, And Balance Point

Explanation
To find the mean, we add up all the values and divide by the total number of values. In this case, we have 8 values. Adding them up, we get 34 + 48 + 21 + 38 + 12 + 52 + 48 + 88 = 341. Dividing this sum by 8, we get 341/8 = 42.625. The closest value to this mean is 43, which is the correct answer.

Explanation
The value 32 will change the mean the most if it was not included because it is the smallest value in the list. Removing the smallest value from a set of numbers will typically have a larger impact on the mean compared to removing a larger value.

Explanation
The median is the measure of central tendency that will have the highest result in this case. The median is the middle value when the data is arranged in ascending or descending order. In this data set, when arranged in ascending order, the median would be 29, which is higher than any of the other values. Therefore, the median has the highest result among the measures of central tendency in this scenario.

Explanation
The mode is the measure of central tendency that represents the most frequently occurring value in a dataset. In this case, finding the mode of the survey responses would indicate the movie that was mentioned the most by the students as their favorite. Therefore, the mode would show the most popular movie among the surveyed students.

Explanation
When one number is significantly lower or higher than the rest, it can greatly affect the mean, which is the average of all the numbers. The median, on the other hand, is the middle value when the numbers are arranged in order. It is not influenced by extreme values, making it a more reliable measure of center in this scenario. Therefore, the median is the best choice when one number is way too low or too high.

Explanation
The average in this context refers to the mean, which is calculated by adding up all the values and dividing by the total number of values. In this case, the chart shows the number of customers at different times, so the average would be calculated by adding up the number of customers at each time and dividing by the total number of times shown in the chart. This would give us the mean number of customers at the Main Street Diner.

Explanation
The given chart shows the amount of money Andy spent on fast food each night. To determine the true statement, we need to compare the median and mean. The median is the middle value in a set of data, while the mean is the average. Since the median is larger than the mean, it means that there are some nights when Andy spent a significantly higher amount on fast food, which skews the data and increases the median. Therefore, the statement "The median is larger than the mean" is true.

Explanation
The balance point is the value that divides the set of numbers into two equal parts. To find the balance point, we need to calculate the average of all the numbers in the set. Adding up all the numbers and dividing by the total count, we get a sum of 298 and a count of 7. Dividing 298 by 7 gives us an average of 42.57. Rounding this to the nearest decimal, we get the balance point of 42.5.

Explanation
The mean would be unfair to use when telling the person being interviewed about how the job pays because it can be heavily influenced by extreme values, such as the worker making $29.85 per hour. This outlier can skew the average and give an inaccurate representation of the typical pay for the job.

Explanation
The statement "The median and mean are always close together" is false. The median and mean can be close together in some cases, but they can also be significantly different in other cases. The median is the middle value in a dataset when it is arranged in order, while the mean is the average of all the values. If there are extreme values or outliers in the dataset, the mean can be greatly affected, causing it to be different from the median. Therefore, the median and mean are not always close together.