Math / Data & Statistics

QuestionExample: If the Quiz scores in a class with 10 students are: $3,5,5,6,4,3,2,1,5,6$ , find the arithmetic mean, median, mode, and range for these scores.

Studdy Solution

STEP 1

What is this asking? We need to find the average, middle score, most frequent score, and the spread of quiz scores. Watch out! Don't mix up the median and the mode!
The median is the middle value when the numbers are sorted, and the mode is the value that appears most often.

STEP 2

1. Calculate the Mean
2. Find the Median
3. Determine the Mode
4. Calculate the Range

STEP 3

Alright, let's kick things off by finding the mean, which is just a fancy word for the average!
To do this, we add up all the scores and then divide by the number of scores.
Super straightforward!

STEP 4

$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$

STEP 5

We have $10$ scores, and they are $3, 5, 5, 6, 4, 3, 2, 1, 5, 6$ .
Let's add 'em up! $3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40$

STEP 6

Now, we divide this sum by the number of scores, which is $10$ . $\text{Mean} = \frac{40}{10} = 4$ So, the mean score is $4$ !

STEP 7

Next up, the median!
This is the middle score when the scores are arranged in order.
Let's sort our scores from lowest to highest: $1, 2, 3, 3, 4, 5, 5, 5, 6, 6$

STEP 8

Since we have an even number of scores ( $10$ ), the median is the average of the two middle scores.
In our sorted list, the two middle scores are $4$ and $5$ .

STEP 9

Let's find the average of these two middle scores: $\text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5$ The median score is $4.5$ !

STEP 10

Now for the mode!
This is the score that appears most frequently.
Looking at our sorted list: $1, 2, 3, 3, 4, 5, 5, 5, 6, 6$ We see that the number $5$ appears three times, which is more than any other number.

STEP 11

So, the mode score is $5$ !

STEP 12

Finally, the range!
This tells us how spread out the scores are.
It's simply the difference between the highest and lowest scores.

STEP 13

In our sorted list, the highest score is $6$ and the lowest score is $1$ . $\text{Range} = \text{Highest score} - \text{Lowest score}$ $\text{Range} = 6 - 1 = 5$ The range of the scores is $5$ !

STEP 14

The mean is $4$ , the median is $4.5$ , the mode is $5$ , and the range is $5$ .

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QuestionExample: If the Quiz scores in a class with 10 students are: $3,5,5,6,4,3,2,1,5,6$ , find the arithmetic mean, median, mode, and range for these scores.

Studdy Solution

STEP 1

What is this asking? We need to find the average, middle score, most frequent score, and the spread of quiz scores. Watch out! Don't mix up the median and the mode!
The median is the middle value when the numbers are sorted, and the mode is the value that appears most often.

STEP 2

1. Calculate the Mean
2. Find the Median
3. Determine the Mode
4. Calculate the Range

STEP 3

Alright, let's kick things off by finding the mean, which is just a fancy word for the average!
To do this, we add up all the scores and then divide by the number of scores.
Super straightforward!

STEP 4

$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$

STEP 5

We have $10$ scores, and they are $3, 5, 5, 6, 4, 3, 2, 1, 5, 6$ .
Let's add 'em up! $3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40$

STEP 6

Now, we divide this sum by the number of scores, which is $10$ . $\text{Mean} = \frac{40}{10} = 4$ So, the mean score is $4$ !

STEP 7

Next up, the median!
This is the middle score when the scores are arranged in order.
Let's sort our scores from lowest to highest: $1, 2, 3, 3, 4, 5, 5, 5, 6, 6$

STEP 8

Since we have an even number of scores ( $10$ ), the median is the average of the two middle scores.
In our sorted list, the two middle scores are $4$ and $5$ .

STEP 9

Let's find the average of these two middle scores: $\text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5$ The median score is $4.5$ !

STEP 10

Now for the mode!
This is the score that appears most frequently.
Looking at our sorted list: $1, 2, 3, 3, 4, 5, 5, 5, 6, 6$ We see that the number $5$ appears three times, which is more than any other number.

STEP 11

So, the mode score is $5$ !

STEP 12

Finally, the range!
This tells us how spread out the scores are.
It's simply the difference between the highest and lowest scores.

STEP 13

In our sorted list, the highest score is $6$ and the lowest score is $1$ . $\text{Range} = \text{Highest score} - \text{Lowest score}$ $\text{Range} = 6 - 1 = 5$ The range of the scores is $5$ !

STEP 14

The mean is $4$ , the median is $4.5$ , the mode is $5$ , and the range is $5$ .

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QuestionExample: If the Quiz scores in a class with 10 students are: 3,5,5,6,4,3,2,1,5,63,5,5,6,4,3,2,1,5,63,5,5,6,4,3,2,1,5,6, find the arithmetic mean, median, mode, and range for these scores.

Studdy Solution

STEP 1

What is this asking? We need to find the average, middle score, most frequent score, and the spread of quiz scores. Watch out! Don't mix up the median and the mode!The median is the middle value when the numbers are sorted, and the mode is the value that appears most often.

STEP 2

1. Calculate the Mean2. Find the Median3. Determine the Mode4. Calculate the Range

STEP 3

Alright, let's **kick things off** by finding the **mean**, which is just a fancy word for the average!To do this, we **add up all the scores** and then **divide by the number of scores**.Super straightforward!

STEP 4

Mean=Sum of all scoresNumber of scores \text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}} Mean=Number of scoresSum of all scores​

STEP 5

We have 101010 scores, and they are 3,5,5,6,4,3,2,1,5,63, 5, 5, 6, 4, 3, 2, 1, 5, 63,5,5,6,4,3,2,1,5,6.Let's add 'em up! 3+5+5+6+4+3+2+1+5+6=40 3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40 3+5+5+6+4+3+2+1+5+6=40

STEP 6

Now, we **divide this sum by the number of scores**, which is 101010. Mean=4010=4 \text{Mean} = \frac{40}{10} = 4 Mean=1040​=4 So, the **mean score is** 444!

STEP 7

Next up, the **median**!This is the **middle score** when the scores are arranged in order.Let's **sort our scores** from lowest to highest: 1,2,3,3,4,5,5,5,6,6 1, 2, 3, 3, 4, 5, 5, 5, 6, 6 1,2,3,3,4,5,5,5,6,6

STEP 8

Since we have an **even number of scores** (101010), the median is the average of the two middle scores.In our sorted list, the two middle scores are 444 and 555.

STEP 9

Let's find the **average of these two middle scores**: Median=4+52=92=4.5 \text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5 Median=24+5​=29​=4.5 The **median score is** 4.54.54.5!

STEP 10

Now for the **mode**!This is the score that appears **most frequently**.Looking at our sorted list: 1,2,3,3,4,5,5,5,6,6 1, 2, 3, 3, 4, 5, 5, 5, 6, 6 1,2,3,3,4,5,5,5,6,6 We see that the number 555 appears three times, which is more than any other number.

STEP 11

So, the **mode score is** 555!

STEP 12

Finally, the **range**!This tells us how spread out the scores are.It's simply the **difference between the highest and lowest scores**.

STEP 13

In our sorted list, the **highest score is** 666 and the **lowest score is** 111. Range=Highest score−Lowest score \text{Range} = \text{Highest score} - \text{Lowest score} Range=Highest score−Lowest score Range=6−1=5 \text{Range} = 6 - 1 = 5 Range=6−1=5The **range of the scores is** 555!

STEP 14

The mean is 444, the median is 4.54.54.5, the mode is 555, and the range is 555.

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QuestionExample: If the Quiz scores in a class with 10 students are: $3,5,5,6,4,3,2,1,5,6$ , find the arithmetic mean, median, mode, and range for these scores.

What is this asking? We need to find the average, middle score, most frequent score, and the spread of quiz scores. Watch out! Don't mix up the median and the mode!
The median is the middle value when the numbers are sorted, and the mode is the value that appears most often.

1. Calculate the Mean
2. Find the Median
3. Determine the Mode
4. Calculate the Range

Alright, let's kick things off by finding the mean, which is just a fancy word for the average!
To do this, we add up all the scores and then divide by the number of scores.
Super straightforward!

$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$

We have $10$ scores, and they are $3, 5, 5, 6, 4, 3, 2, 1, 5, 6$ .
Let's add 'em up! $3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40$

Now, we divide this sum by the number of scores, which is $10$ . $\text{Mean} = \frac{40}{10} = 4$ So, the mean score is $4$ !

Next up, the median!
This is the middle score when the scores are arranged in order.
Let's sort our scores from lowest to highest: $1, 2, 3, 3, 4, 5, 5, 5, 6, 6$

Since we have an even number of scores ( $10$ ), the median is the average of the two middle scores.
In our sorted list, the two middle scores are $4$ and $5$ .

Let's find the average of these two middle scores: $\text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5$ The median score is $4.5$ !

Now for the mode!
This is the score that appears most frequently.
Looking at our sorted list: $1, 2, 3, 3, 4, 5, 5, 5, 6, 6$ We see that the number $5$ appears three times, which is more than any other number.

So, the mode score is $5$ !

Finally, the range!
This tells us how spread out the scores are.
It's simply the difference between the highest and lowest scores.

In our sorted list, the highest score is $6$ and the lowest score is $1$ . $\text{Range} = \text{Highest score} - \text{Lowest score}$ $\text{Range} = 6 - 1 = 5$ The range of the scores is $5$ !

The mean is $4$ , the median is $4.5$ , the mode is $5$ , and the range is $5$ .