Solved on Sep 19, 2023

Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. $300.6, 231.5, 135.0, 10$ or $271, 217, 272, 5$ or $32, 32, 35, 10$ or $18.2, 20, 20, 5$ .

STEP 1

Assumptions1. The stem-and-leaf plot represents the data in hundreds, tens, and units. . The stem represents hundreds and the leaf represents tens and units.
3. The data is represented in the format of stem|leaf.

STEP 2

First, we need to retrieve the original data from the stem-and-leaf plot. This can be done by multiplying the stem by100 and adding the leaf to it.

STEP 3

Retrieve the data from the first row.
$105|3535 =1050,1053,1053,1055$

STEP 4

Retrieve the data from the second row.
$202|313240 =2020,2023,2021,2023,2024,2020$

STEP 5

Retrieve the data from the third row.
There is no leaf in the third row, so the data is just the stem, which is300.

STEP 6

Retrieve the data from the fourth row.
$4|32 =400,402$

STEP 7

Retrieve the data from the fifth row.
$5|4252 =500,504,502,505$

STEP 8

Now that we have retrieved all the data, we can list them in ascending order.
$1050,1053,1053,1055,2020,2023,2021,2023,2024,2020,300,400,402,500,504,502,505$

STEP 9

Now, we can calculate the mean of the data. The mean is the sum of all the data divided by the number of data points.
$Mean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}$

STEP 10

Calculate the sum of all the data.
$Sum\, of\, all\, data =1050 +1053 +1053 +1055 +2020 +2023 +202 +2023 +2024 +2020 +300 +400 +402 +500 +504 +502 +505$

STEP 11

Calculate the number of data points.
There are17 data points.

STEP 12

Calculate the mean.
$Mean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}$

STEP 13

Next, we can calculate the median of the data. The median is the middle value when the data is listed in ascending order. If there is an even number of data points, the median is the average of the two middle values.

STEP 14

Since there are17 data points, the median is the9th value.

STEP 15

Find the9th value in the data.
The9th value is2023.

STEP 16

Next, we can calculate the mode of the data. The mode is the value that appears most frequently in the data.

STEP 17

Find the value that appears most frequently in the data.
The value1053 appears twice, the value2020 appears twice, and the value2023 appears twice. So, there are three modes1053,2020, and2023.

STEP 18

Finally, we can find the sample size of the data. The sample size is simply the number of data points.
The sample size is17.
The mean, median, mode, and sample size of the distribution are $271,2023,1053,2020,2023,17$ .

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Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. $300.6, 231.5, 135.0, 10$ or $271, 217, 272, 5$ or $32, 32, 35, 10$ or $18.2, 20, 20, 5$ .

STEP 1

Assumptions1. The stem-and-leaf plot represents the data in hundreds, tens, and units. . The stem represents hundreds and the leaf represents tens and units.
3. The data is represented in the format of stem|leaf.

STEP 2

First, we need to retrieve the original data from the stem-and-leaf plot. This can be done by multiplying the stem by100 and adding the leaf to it.

STEP 3

Retrieve the data from the first row.
$105|3535 =1050,1053,1053,1055$

STEP 4

Retrieve the data from the second row.
$202|313240 =2020,2023,2021,2023,2024,2020$

STEP 5

Retrieve the data from the third row.
There is no leaf in the third row, so the data is just the stem, which is300.

STEP 6

Retrieve the data from the fourth row.
$4|32 =400,402$

STEP 7

Retrieve the data from the fifth row.
$5|4252 =500,504,502,505$

STEP 8

Now that we have retrieved all the data, we can list them in ascending order.
$1050,1053,1053,1055,2020,2023,2021,2023,2024,2020,300,400,402,500,504,502,505$

STEP 9

Now, we can calculate the mean of the data. The mean is the sum of all the data divided by the number of data points.
$Mean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}$

STEP 10

Calculate the sum of all the data.
$Sum\, of\, all\, data =1050 +1053 +1053 +1055 +2020 +2023 +202 +2023 +2024 +2020 +300 +400 +402 +500 +504 +502 +505$

STEP 11

Calculate the number of data points.
There are17 data points.

STEP 12

Calculate the mean.
$Mean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}$

STEP 13

Next, we can calculate the median of the data. The median is the middle value when the data is listed in ascending order. If there is an even number of data points, the median is the average of the two middle values.

STEP 14

Since there are17 data points, the median is the9th value.

STEP 15

Find the9th value in the data.
The9th value is2023.

STEP 16

Next, we can calculate the mode of the data. The mode is the value that appears most frequently in the data.

STEP 17

Find the value that appears most frequently in the data.
The value1053 appears twice, the value2020 appears twice, and the value2023 appears twice. So, there are three modes1053,2020, and2023.

STEP 18

Finally, we can find the sample size of the data. The sample size is simply the number of data points.
The sample size is17.
The mean, median, mode, and sample size of the distribution are $271,2023,1053,2020,2023,17$ .

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Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. 300.6,231.5,135.0,10300.6, 231.5, 135.0, 10300.6,231.5,135.0,10 or 271,217,272,5271, 217, 272, 5271,217,272,5 or 32,32,35,1032, 32, 35, 1032,32,35,10 or 18.2,20,20,518.2, 20, 20, 518.2,20,20,5.

STEP 1

Assumptions1. The stem-and-leaf plot represents the data in hundreds, tens, and units. . The stem represents hundreds and the leaf represents tens and units.3. The data is represented in the format of stem|leaf.

STEP 2

First, we need to retrieve the original data from the stem-and-leaf plot. This can be done by multiplying the stem by100 and adding the leaf to it.

STEP 3

Retrieve the data from the first row.105∣3535=1050,1053,1053,1055105|3535 =1050,1053,1053,1055105∣3535=1050,1053,1053,1055

STEP 4

Retrieve the data from the second row.202∣313240=2020,2023,2021,2023,2024,2020202|313240 =2020,2023,2021,2023,2024,2020202∣313240=2020,2023,2021,2023,2024,2020

STEP 5

Retrieve the data from the third row.There is no leaf in the third row, so the data is just the stem, which is300.

STEP 6

Retrieve the data from the fourth row.4∣32=400,4024|32 =400,4024∣32=400,402

STEP 7

Retrieve the data from the fifth row.5∣4252=500,504,502,5055|4252 =500,504,502,5055∣4252=500,504,502,505

STEP 8

STEP 9

Now, we can calculate the mean of the data. The mean is the sum of all the data divided by the number of data points.Mean=Sum of all dataNumber of data pointsMean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}Mean=NumberofdatapointsSumofalldata​

STEP 10

STEP 11

Calculate the number of data points.There are17 data points.

STEP 12

Calculate the mean.Mean=Sum of all dataNumber of data pointsMean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}Mean=NumberofdatapointsSumofalldata​

STEP 13

Next, we can calculate the median of the data. The median is the middle value when the data is listed in ascending order. If there is an even number of data points, the median is the average of the two middle values.

STEP 14

Since there are17 data points, the median is the9th value.

STEP 15

Find the9th value in the data.The9th value is2023.

STEP 16

Next, we can calculate the mode of the data. The mode is the value that appears most frequently in the data.

STEP 17

Find the value that appears most frequently in the data.The value1053 appears twice, the value2020 appears twice, and the value2023 appears twice. So, there are three modes1053,2020, and2023.

STEP 18

Finally, we can find the sample size of the data. The sample size is simply the number of data points.The sample size is17.The mean, median, mode, and sample size of the distribution are 271,2023,1053,2020,2023,17271,2023,1053,2020,2023,17271,2023,1053,2020,2023,17.

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Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. $300.6, 231.5, 135.0, 10$ or $271, 217, 272, 5$ or $32, 32, 35, 10$ or $18.2, 20, 20, 5$ .

Assumptions1. The stem-and-leaf plot represents the data in hundreds, tens, and units. . The stem represents hundreds and the leaf represents tens and units.
3. The data is represented in the format of stem|leaf.

Retrieve the data from the first row.
$105|3535 =1050,1053,1053,1055$

Retrieve the data from the second row.
$202|313240 =2020,2023,2021,2023,2024,2020$

Retrieve the data from the third row.
There is no leaf in the third row, so the data is just the stem, which is300.

Retrieve the data from the fourth row.
$4|32 =400,402$

Retrieve the data from the fifth row.
$5|4252 =500,504,502,505$

Now, we can calculate the mean of the data. The mean is the sum of all the data divided by the number of data points.
$Mean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}$

Calculate the number of data points.
There are17 data points.

Calculate the mean.
$Mean = \frac{Sum\, of\, all\, data}{Number\, of\, data\, points}$

Find the9th value in the data.
The9th value is2023.

Find the value that appears most frequently in the data.
The value1053 appears twice, the value2020 appears twice, and the value2023 appears twice. So, there are three modes1053,2020, and2023.

Finally, we can find the sample size of the data. The sample size is simply the number of data points.
The sample size is17.
The mean, median, mode, and sample size of the distribution are $271,2023,1053,2020,2023,17$ .