Answer :
Sure! Let's go through the step-by-step solution for finding the mean, median, mode, and range of the points Jaiden scored in her last 9 basketball games. The points are:
20, 21, 18, 22, 13, 15, 20, 19, 23
1. Mean:
The mean is the average of all the numbers. To find it, sum all the points and divide by the number of games.
[tex]\[ \text{Mean} = \frac{20 + 21 + 18 + 22 + 13 + 15 + 20 + 19 + 23}{9} \][/tex]
Performing the addition:
[tex]\[ 20 + 21 + 18 + 22 + 13 + 15 + 20 + 19 + 23 = 171 \][/tex]
Now, divide by the number of games:
[tex]\[ \text{Mean} = \frac{171}{9} = 19.0 \][/tex]
2. Median:
The median is the middle value when the numbers are sorted in ascending order. First, arrange the points in ascending order:
[tex]\[ 13, 15, 18, 19, 20, 20, 21, 22, 23 \][/tex]
Since there are 9 values (an odd number), the median is the middle one, which is the 5th value in the sorted list:
[tex]\[ \text{Median} = 20 \][/tex]
3. Mode:
The mode is the number that appears most frequently. Checking the points, we see that 20 appears twice while all other numbers appear only once:
[tex]\[ \text{Mode} = 20 \][/tex]
4. Range:
The range is the difference between the highest and lowest values. First, identify the highest and lowest points:
Highest value = 23
Lowest value = 13
Now, calculate the range:
[tex]\[ \text{Range} = 23 - 13 = 10 \][/tex]
Therefore, the correct response, given these calculations, is:
Mean = 19, Median = 20, Mode = 20, Range = 10
So, the correct answer from the given options is:
```
Mean 19, Median = 20, Mode = 20, Range = 10
```
20, 21, 18, 22, 13, 15, 20, 19, 23
1. Mean:
The mean is the average of all the numbers. To find it, sum all the points and divide by the number of games.
[tex]\[ \text{Mean} = \frac{20 + 21 + 18 + 22 + 13 + 15 + 20 + 19 + 23}{9} \][/tex]
Performing the addition:
[tex]\[ 20 + 21 + 18 + 22 + 13 + 15 + 20 + 19 + 23 = 171 \][/tex]
Now, divide by the number of games:
[tex]\[ \text{Mean} = \frac{171}{9} = 19.0 \][/tex]
2. Median:
The median is the middle value when the numbers are sorted in ascending order. First, arrange the points in ascending order:
[tex]\[ 13, 15, 18, 19, 20, 20, 21, 22, 23 \][/tex]
Since there are 9 values (an odd number), the median is the middle one, which is the 5th value in the sorted list:
[tex]\[ \text{Median} = 20 \][/tex]
3. Mode:
The mode is the number that appears most frequently. Checking the points, we see that 20 appears twice while all other numbers appear only once:
[tex]\[ \text{Mode} = 20 \][/tex]
4. Range:
The range is the difference between the highest and lowest values. First, identify the highest and lowest points:
Highest value = 23
Lowest value = 13
Now, calculate the range:
[tex]\[ \text{Range} = 23 - 13 = 10 \][/tex]
Therefore, the correct response, given these calculations, is:
Mean = 19, Median = 20, Mode = 20, Range = 10
So, the correct answer from the given options is:
```
Mean 19, Median = 20, Mode = 20, Range = 10
```
