Answer :
Answer:
C. The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.
Step-by-step explanation:
In the given image that is representing the number of points that Shira scored, each basketball game so far this season we can observe that the data is skewed to the left.
Lets consider the definition of skewness of a data set:
A left-skewed distribution has a long left tail. Left-skewed distributions are also known as negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. So in this case peak remains on the right side.
A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions because there is a long tail in the positive direction on the number line. So in this case peak remains on the left side.
In our case it can be see that the data has peak on to the right side and hence it is left skewed. Also it can be seen from the dot plot that Shira has never scored fewer than 2 points and the maximum she has scored in a game is 12 points.
Therefore, the data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game
The data is skewed to the left and shows that she scored 11 points in more games than all of the other point values combined. (Option D)
How to identify skewed graph?
A skewed distribution is a distribution having bias on one of the two sides (either left or right).
It is like leaning mountain on one side(left or right).
- A left skewed graph has an elongated tail on the left side of the main mountain like figure. The mountain like figure is after that elongated tail. It is also called negatively skewed graph.
- A right skewed graph has an elongated tail on the right side of the main mountain like figure. The mountain like figure is before that elongated tail. It is also called positively skewed graph.
How does the dot plot work?
Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table. Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.
For this case, the dot plot has tail on left side and then the main mountain like figure on right.
Thus, it is left skewed.
This is correctly identified by option C and D.
Since there are no points before 2, or after 12, so she never scored fewer than 2 points or more than 12 points in a game.
Thus, option C is correct but only for one season, and therefore is wrong about saying that "she never scored fewer than 2 points or more than 12 points in a game." since here the data was all games by her only for one season, and option doesn't specifies that it is talking about that considered season only.
Now, option D tells that:
Total score obtained from 11 point scoring > all other scores combined.
Let we check it.
Total score without 11 points = 2 points twice, 3 point ones, 5 point ones and so on, 12 point ones (without counting 11 points).
Thus, we get:
Total score without 11 points = [tex]2\times 2+ 3\times1 + 5 \times 1 + 7 \times 2 + 9 \times 3 + 12 \times 1 = 65[/tex]
There are 6 dots over 11, so 11 points was scored 6 times, which means:
Scores obtained from 11 points' scoring = [tex]6 \times 11 = 66[/tex]
We see that 66 > 65, so Option D is entirely correct.
Thus, the data is skewed to the left and shows that she scored 11 points in more games than all of the other point values combined. (Option D)
Learn more about dot plot here:
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