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Organize the following data in a stem-and-leaf plot:

219, 151, 199, 186, 170, 186, 194, 184, 196, 185, 174, 186, 197, 170, 178, 179, 182, 193, 195, 171

b) Use your stem-and-leaf plot to determine the median and the mode.

c) Calculate the mean of the data.

Answer :

The stem-and-leaf plot for the data is organized by breaking each number into a stem and a leaf. The median value is 185.5, the mode is 186, and the mean is 190.1.

To organize the data into a stem-and-leaf plot, we need to break each number into a stem (the first part of the number) and a leaf (the last digit). Here's the data: 219, 151, 199, 186, 170, 186, 194, 184, 196, 185, 174, 186, 197, 170, 178, 179, 182, 193, 195, 171.

Stem-and-Leaf Plot:

15 | 1
17 | 0, 0, 1, 4, 8, 9
18 | 2, 4, 5, 6, 6, 6
19 | 3, 4, 5, 6, 7, 9
21 | 9

Calculating Median and Mode

To find the median, we list the values in order: 151, 170, 170, 171, 174, 178, 179, 182, 184, 185, 186, 186, 186, 193, 194, 195, 196, 197, 199, 219.

There are 20 values, so the median is the average of the 10th and 11th values: (185+186)/2 = 185.5.

The mode is the value that appears most frequently, which is 186 (it appears 3 times).

Calculating Mean

To find the mean, add all the values and divide by the number of values:

(219 + 151 + 199 + 186 + 170 + 186 + 194 + 184 + 196 + 185 + 174 + 186 + 197 + 170 + 178 + 179 + 182 + 193 + 195 + 171) / 20 = 190.1.

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Rewritten by : Barada

a) To create a stem-and-leaf plot, we need to separate each number into a stem and a leaf. The stem is the digit(s) to the left of the rightmost digit, and the leaf is the rightmost digit. For example, 219 would have a stem of 21 and a leaf of 9. The stem-and-leaf plot for this data is:

```
15 | 1
17 | 0 0 1 4
18 | 2 4 5 6 6
19 | 3 4 5 6 7 9
```

b) To find the median, we need to put the data in order from least to greatest:

```
151 170 170 171 174 178 179 182 184 185 186 186 186 193 194 195 196 197 199 219
```

There are 20 numbers in the data set, so the median is the average of the 10th and 11th numbers:

```
Median = (185 + 186) / 2 = 185.5
```

To find the mode, we look for the most common value in the data set. In this case, the stem-and-leaf plot shows that there are two modes: 186 and 170.

c) To calculate the mean, we add up all the numbers and divide by the total number of numbers:

```
Mean = (219 + 151 + 199 + 186 + 170 + 186 + 194 + 184 + 196 + 185 + 174 + 186 + 197 + 170 + 178 + 179 + 182 + 193 + 195 + 171) / 20
Mean = 1849 / 20
Mean = 92.45
```

Therefore, the mean of the data is 92.45.