QuestionFind the mean, median, and mode of the data from this stem-and-leaf plot: 0 | 4, 1 | 55, 2 | 4578, 3 | 2.

Studdy Solution

STEP 1

Assumptions1. The stem-and-leaf plot represents the data as follows $\begin{array}{l|l} 0 &4 \\ 1 &55 \\ &4578 \\ 3 &\end{array}$ . The leaf represents the ones digit, and the stem represents the tens digit.

STEP 2

First, we need to list out all the data points from the stem-and-leaf plot. $Data = [4,15,15,24,25,27,28,32]$

STEP 3

To find the mean, we need to add up all the data points and divide by the number of data points. $Mean = \frac{Sum\, of\, all\, data\, points}{Number\, of\, data\, points}$

STEP 4

Now, plug in the values for the sum of all data points and the number of data points to calculate the mean.
$Mean = \frac{4 +15 +15 +24 +25 +27 +28 +32}{8}$

STEP 5

Calculate the mean.
$Mean = \frac{170}{8} =21.25$

STEP 6

To find the median, we need to list the data points in ascending order and find the middle value. If there are an even number of data points, the median is the average of the two middle values.
$Median = Middle\, value\, of\, the\, ordered\, data$

STEP 7

The data points are already in ascending order. Since there are data points, an even number, we need to find the average of the4th and5th data points.
$Median = \frac{4th\, data\, point +5th\, data\, point}{2}$

STEP 8

Plug in the values for the4th and5th data points to calculate the median.
$Median = \frac{24 +25}{2}$

STEP 9

Calculate the median.
$Median = \frac{49}{2} =24.5$

STEP 10

To find the mode, we need to find the data point(s) that occur most frequently.
$Mode = Most\, frequently\, occurring\, data\, point(s)$

STEP 11

From the data, we can see that the number15 occurs twice, while all other numbers occur only once. Therefore, the mode is15.
Mean21.3 (rounded to one decimal place) Median24.5Mode15

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms