Question

How do you find the mean, median and mode of: 7, 3, 2, 1, 13, 8, 1, 5, 14, 11, 15?

Answer 1

Hint: To determine the mean, median, mode of the provided data sets, we will first define each of them. And then calculate mean, median, mode using the definitions and formulas. One important thing to notice is that we are dealing with ungrouped data.

Complete answer:
We will first understand the concept of mean, median and mode.
Mean: The average of all the terms in a particular data collection is called the mean of the data set.
The formula of mean is \[Mean = \dfrac{{{\text{Sum of all the term in given set}}}}{{{\text{Total number of terms in that set}}}}\]
Median: The median of a data set is the value that falls exactly in the centre of the set when it is arranged in ascending order.
The formula of median when number of terms is odd \[Median = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}term\]
When number of terms is even \[Median = \dfrac{{{{\left( {\dfrac{n}{2}} \right)}^{th}}term + {{\left( {\dfrac{n}{2} + 1} \right)}^{th}}term}}{2}\]
Mode: The term that appears the most in a particular data collection is referred to as the data set's mode.
Now, we will calculate the mean, median, mode
We know that \[Mean = \dfrac{{{\text{Sum of all the term in given set}}}}{{{\text{Total number of terms in that set}}}}\]
$Mean = \dfrac{{7 + 3 + 2 + 1 + 13 + 8 + 1 + 5 + 14 + 11 + 15}}{{11}}$
$Mean = \dfrac{{80}}{{11}}$
We will now organise the data in ascending order before computing the median, mean.
We will arrange the data in ascending order: 1, 1, 2, 3, 5, 7, 8, 11, 13, 14, 15
we can see that the total number of terms is 11, which is odd, and we can also observe that when the number of terms is odd.
\[Median = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}term\]
\[Median = {\left( {\dfrac{{11 + 1}}{2}} \right)^{th}}term\]\[Median = {6^{th}}termMean = \dfrac{{80}}{{11}}\]
\[Median = {\left( 6 \right)^{th}}term\]
We can get the \[{6^{th}}term\] in the sequence 1, 1, 2, 3, 5, 7, 8, 11, 13, 14, 15 is 7.
So, median is 7
We'll now compute the mode. As we can see from the definition of mode above, mode is the number that appears the most frequently in the data collection.
So, the most frequent term in the sequence 1, 1, 2, 3, 5, 7, 8, 11, 13, 14, 15 is 1.
Hence, the mean, median and mode are \[\dfrac{{80}}{{11}}\] , 7 and 1 respectively.

Note: While calculating the median of a given data set, it is critical that the data set be arranged in ascending order; otherwise, students will not obtain the proper result, and there is a high risk of making mistakes when creating sets, so students must be cautious.