Question

the frequency table summarizes a data - set of the weights, rounded to the nearest pound, of 71 tortoises. a weight of 19 pounds is added to the original data set, creating a new data set of the weights, rounded to the nearest pound, of 72 tortoises. which statement best compares the mean and median of the new data set to the mean and median of the original data set?
a) the mean of the new data set is greater than the mean of the original data set, and the median of the new data set is greater than the median of the original data set.
b) the mean of the new data set is greater than the mean of the original data set, and the medians of the two data sets are equal.
c) the mean of the new data set is less than the mean of the original data set, and the median of the new data set is less than the median of the original data set.
d) the mean of the new data set is less than the mean of the original data set, and the medians of the two data sets are equal.
s - 29=(x - a)(x - 29)
which of the following are solutions to the given equation, where a is a constant and a>30?
i. a
ii. a + 1
iii. 29
a) i and ii only
b) i and iii only
c) ii and iii only
d) i, ii, and iii
in the xy - plane, the graph of the equation y=-x²+9x - 100 intersects the line y = c at exactly one point. what is the value of c?
a) -\frac{481}{4}
b) - 100
c) -\frac{319}{4}
d) -\frac{9}{2}

Explanation:

Step1: Analyze the mean change

The original data - set has 71 data points. When a value (19 pounds) is added, since the mean is the sum of all values divided by the number of values, and 19 is likely a non - extreme value in the context of the data set, adding a value to the data set will increase the sum and the number of data points. The mean of the new data set (with 72 data points) will be greater than the mean of the original data set (with 71 data points) because the added value is non - zero.

Step2: Analyze the median change

The original data set has 71 (an odd number) data points. The median is the middle - numbered value when the data is arranged in ascending order. When we add one more data point (making it 72, an even number), the median is the average of the two middle - numbered values. Since 19 is just one more data point and not an extreme outlier, the position of the middle values in the ordered data set does not change in a way that would affect the median value significantly. In fact, for a symmetric or near - symmetric distribution of data around the median, the medians of the two data sets are equal.

Answer:

B) The mean of the new data set is greater than the mean of the original data set, and the medians of the two data sets are equal.