Question

the following data shows the car speed each student went the past week. 35, 55, 75, 75, 75, 75, 80, 20, 100, 65, 70, 80, 90, 75, 80 calculate the mean and the median, then convert the data into a dot - plot. refer to the data. select true if the statement accurately describes the data. select false if the statement does not accurately represent the data.
statement
true or false
statement a: the mean is higher than the median
statement b: the data shows a skewed left distribution
statement c: removing the number 35 from the data set will increase the mean, but not change the median.
statement d: adding a number greater than the mean will result in neither the mean or median changing.
for each statement, highlight one or two vocab word/key word. then write a small summary on what the question wants us to find.
statement a: asking us:
statement b: asking us:
statement c: asking us:
statement d: asking us:
for each response you selected, “false” explains your reasoning.

Explanation:

Step1: Calculate the mean

The data set is [35, 55, 75, 75, 75, 80, 20, 100, 65, 70, 80, 90, 75, 80]. The sum of the data values is $35 + 55+75+75+75+80+20+100+65+70+80+90+75+80=995$. There are $n = 14$ data - points. The mean $\bar{x}=\frac{995}{14}\approx71.07$.

Step2: Calculate the median

First, order the data set: [20, 35, 55, 65, 70, 75, 75, 75, 75, 80, 80, 80, 90, 100]. Since $n = 14$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The 7th and 8th values are 75 and 75, so the median $M=\frac{75 + 75}{2}=75$. Since $71.07<75$, statement A is False.

Step3: Analyze the skewness

In a left - skewed distribution, the tail is on the left side. The lower values (20 and 35) pull the mean down. Since the mean is less than the median, it indicates a left - skewed distribution, so statement B is True.

Step4: Analyze the effect of removing 35

The new sum of the data values (after removing 35) is $995−35 = 960$. There are $n = 13$ data - points. The new mean is $\frac{960}{13}\approx73.85$, which is greater than the original mean. The ordered data set without 35 is [20, 55, 65, 70, 75, 75, 75, 75, 80, 80, 80, 90, 100]. Since $n = 13$ (an odd number), the median is the 7th value, which is 75, same as the original median. So statement C is True.

Step5: Analyze the effect of adding a number greater than the mean

If we add a number greater than the mean, the sum of the data values will increase and so will the mean. For example, if we add 80 (greater than 71.07), the new sum is $995 + 80=1075$, and the new number of data - points is $n = 15$. The new mean is $\frac{1075}{15}\approx71.67$. Depending on the value added, the median may or may not change. But in general, adding a value greater than the mean will change the mean. So statement D is False.

Answer:

Statement A: False
Statement B: True
Statement C: True
Statement D: False