Question

5. Respond to the following questions about statistics.(a) Find the mean, median, and mode of the following dataset:{10,20, 42, 22, 56, 42, 3, 89, 42, 70,20}

Answer 1

• Mean: 37.82
• Median: 42
• Mode: 42

In-depth explanation:

Hi! This question is asking us to find the mean, median, and mode of this dataset.

Let's start with the mean.

What is the mean? The mean is the average of the dataset.

To find the mean, we add all the data values and divide by how many there are.

For this set, the values are: 10, 20, 42, 22, 56, 42, 3, 89, 42, 70, 20.

So we add them: 10 + 20 + 42 + 22 + 56 + 42 + 3 + 89 + 42 + 70 + 20 = 416.

Then, we divide by how many there are: 11

416 ÷ 11 ≈ 37.82

Therefore, the mean of this set is 37.82.

`\rule{350}{1}`

Now let's move on to the median.

But before we find the median, we will arrange the values of the set in ascending order (from least to greatest).

3, 10, 20, 20, 22, 42, 42, 42, 56, 70, 89

Now, find the number in the middle: 42

`\rule{350}{1}`

Now let's move on the mode.

The mode is simply the number that occurs the most.

In this case, the number that occurs the most is 42.

Therefore, 42 is the mode.

Answer 2

Given:

A data set: {10,20, 42, 22, 56, 42, 3, 89, 42, 70,20}.

TO find:

The mean, median and mode.

Solution:

The mean of a data set is given by:

`Mean=\frac{\text{ sum of all observations}}{\text{ number of observations}}`

So, the mean for the given data set is:

`\begin{gathered} Mean=(10+20+42+22+56+42+3+89+42+70+20)/(11) \\ =(416)/(11) \\ =37.82 \end{gathered}`

To find the median, first change them into ascending order as

3, 10, 20, 20, 22, 42, 42, 42, 56, 70, 89.

Now, the number of observations is odd. So, the median of the data set is:

`\begin{gathered} Median=(n+1)/(2)th\text{ term} \\ =(11+1)/(2)th\text{ term} \\ =6th\text{ term} \\ =42 \end{gathered}`

Now, the element whose frequency is maximum is the mode of the given data set. Here, the frequency of 42 is maximum. So, the mode is 42.

Thus, the mean is 37.82, the median is 42 and the mode is 42.