Well, you simply have to take the middle two scores and average the result. So, if we look at the example below:. Only now we have to take the 5th and 6th score in our data set and average them to get a median of The mode is the most frequent score in our data set. On a histogram it represents the highest bar in a bar chart or histogram. You can, therefore, sometimes consider the mode as being the most popular option.
An example of a mode is presented below:. Normally, the mode is used for categorical data where we wish to know which is the most common category, as illustrated below:. We can see above that the most common form of transport, in this particular data set, is the bus. However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency, such as below:.
We are now stuck as to which mode best describes the central tendency of the data. This is particularly problematic when we have continuous data because we are more likely not to have any one value that is more frequent than the other.
For example, consider measuring 30 peoples' weight to the nearest 0. How likely is it that we will find two or more people with exactly the same weight e. The answer, is probably very unlikely - many people might be close, but with such a small sample 30 people and a large range of possible weights, you are unlikely to find two people with exactly the same weight; that is, to the nearest 0. This is why the mode is very rarely used with continuous data. Another problem with the mode is that it will not provide us with a very good measure of central tendency when the most common mark is far away from the rest of the data in the data set, as depicted in the diagram below:.
In the above diagram the mode has a value of 2. We can clearly see, however, that the mode is not representative of the data, which is mostly concentrated around the 20 to 30 value range.
To use the mode to describe the central tendency of this data set would be misleading. We often test whether our data is normally distributed because this is a common assumption underlying many statistical tests. An example of a normally distributed set of data is presented below:. If one score with a value of X 5 21 is Create an Account and Get the Solution. Log into your existing Transtutors account. Have an account already?
Click here to Login. No Account Yet? Click here to Sign Up. Sign in with Facebook. Looking for Something Else? Ask a Similar Question Ask Now. Lets Start. Google Classroom Facebook Twitter. Video transcript - [Voiceover] Let's think about what happens to the median and mean of a set of numbers when I change one of the numbers. And so let's look at this example. A group of four friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game.
Their high scores are all between and , except for Adam, whose high score is Adam then bowls a great game and has a new high score of How will increasing Adam's high score affect the mean and median? Now, like always, pause this video and see if you can figure this out yourself. All right, so let's just think about what they're saying. We have four friends, and they each keep track of their all-time high score, so we're gonna have four data points, an all-time high score for each of the friends.
So let's see, this is the lowest score of the friends, this is the second lowest, second to highest, and this is the highest scoring of the friends. So let's see. So before Adam bowls this super-awesome game, the scores look something like this. The lowest score is Adam scores And if you take Adam out of the picture, the highest score is a People bring different board games to play, A: Given Information : A board game club meets each week at the local library. People bring differe Q: An ecologist is considering two different positions in which to setup his solar energy collector.
Q: In Problem 11 from the previous section, westated that the damage amount is normally distributed The triangular distributi Q: For the majority of maths tests taken at a school, it is shown that the test score is approximaly no A: The normal distribution is the most useful theoretical distribution for continuous variable.
For th Find the A: We need to test Does this indicate that the population proportion of guests who catch pike over 20 p A: Rearranging the values in ascending order, 0. Q: Can you help me with this? A: Probability is a branch of mathematics or statistics which deals the chances of happening an event.
Q: The following data represent the square footage of 10 three-bedroom condos for sale in Hilton Head, A: We first need to rearrange the given data set, ,,,,,,,,, Q: If a researcher is using a t statistic to test a null hypothesis about a population, what informatio A: Values required to calculate t-statistics: 1.
Sample size 2. Sample Mean 3. Sample Variance or Sta Q: The standard deviation of a sample is 3. Q: Consider the five-product line produce products with the same weight grams.
Test the hypothesis of A: If there is homogeneity of variance then we use the Bartlett test. Here we check whether the varianc Q: Assume researchers are trying to find out the mean concentration levels of a specific drug in a popu
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